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Ecuación 3^x=27
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Expresiones idénticas
- x.diff(x)*(y)*((y^ dos)*(x.diff(x)*(y))+ dos *y*x*(y))=l+x
- x.diff(x) multiplicar por (y) multiplicar por ((y al cuadrado ) multiplicar por (x.diff(x) multiplicar por (y)) más 2 multiplicar por y multiplicar por x multiplicar por (y)) es igual a l más x
- x.diff(x) multiplicar por (y) multiplicar por ((y en el grado dos) multiplicar por (x.diff(x) multiplicar por (y)) más dos multiplicar por y multiplicar por x multiplicar por (y)) es igual a l más x
- x.diff(x)*(y)*((y2)*(x.diff(x)*(y))+2*y*x*(y))=l+x
- x.diffx*y*y2*x.diffx*y+2*y*x*y=l+x
- x.diff(x)*(y)*((y²)*(x.diff(x)*(y))+2*y*x*(y))=l+x
- x.diff(x)*(y)*((y en el grado 2)*(x.diff(x)*(y))+2*y*x*(y))=l+x
- x.diff(x)(y)((y^2)(x.diff(x)(y))+2yx(y))=l+x
- x.diff(x)(y)((y2)(x.diff(x)(y))+2yx(y))=l+x
- x.diffxyy2x.diffxy+2yxy=l+x
- x.diffxyy^2x.diffxy+2yxy=l+x
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Expresiones semejantes
- x.diff(x)*(y)*((y^2)*(x.diff(x)*(y))+2*y*x*(y))=l-x
- x.diff(x)*(y)*((y^2)*(x.diff(x)*(y))-2*y*x*(y))=l+x
x.diff(x)*(y)*((y^2)*(x.diff(x)*(y))+2*y*x*(y))=l+x la ecuación
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Solución
Ha introducido
[src]
//x for 0 = 1\ / //x for 0 = 1\ \ || | | 2 || | | |<1 for 1 = 1|*y*|y *|<1 for 1 = 1|*y + 2*y*x*y| = l + x || | | || | | \\0 otherwise/ \ \\0 otherwise/ /
$$y \left(\begin{cases} x & \text{for}\: 0 = 1 \\1 & \text{for}\: 1 = 1 \\0 & \text{otherwise} \end{cases}\right) \left(y^{2} y \left(\begin{cases} x & \text{for}\: 0 = 1 \\1 & \text{for}\: 1 = 1 \\0 & \text{otherwise} \end{cases}\right) + y x 2 y\right) = l + x$$
Gráfica
Respuesta rápida
[src]
// _______________________________________________________________________________________________________ \ // _______________________________________________________________________________________________________ \
|| / _____________________________ | || / _____________________________ |
|| / / / 4\ | || / / / 4\ |
|| / / 2 | 3*x | | || / / 2 | 3*x | |
|| / / 6 x *|-l - x - ----| 3 | || / / 6 x *|-l - x - ----| 3 |
|| / 2 / 3*x \ 16 / 2*x | || / 2 / 3*x \ 16 / 2*x |
|| / 2*x + 2*3 / - ---- - ------------------ + ----------------------------------------------------- | || / 2*x + 2*3 / - ---- - ------------------ + ----------------------------------------------------- |
|| _____________________________________________ / \/ 32 2 _____________________________________________ | || _____________________________________________ / \/ 32 2 _____________________________________________ |
|| / _____________________________ / / _____________________________ | || / _____________________________ / / _____________________________ |
|| / / / 4\ / / / / 4\ | || / / / 4\ / / / / 4\ |
|| / / 2 | 3*x | / / / 2 | 3*x | | || / / 2 | 3*x | / / / 2 | 3*x | |
|| / / 6 x *|-l - x - ----| / / / 6 x *|-l - x - ----| | || / / 6 x *|-l - x - ----| / / / 6 x *|-l - x - ----| |
|| / 2 / 3*x \ 16 / / / 2 / 3*x \ 16 / | || / 2 / 3*x \ 16 / / / 2 / 3*x \ 16 / |
|| / x - 2*3 / - ---- - ------------------ / / x - 2*3 / - ---- - ------------------ | || / x - 2*3 / - ---- - ------------------ / / x - 2*3 / - ---- - ------------------ |
|| x \/ \/ 32 2 \/ \/ \/ 32 2 | || x \/ \/ 32 2 \/ \/ \/ 32 2 |
|| - - - ----------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------- for l + x = 0| || - - - ----------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------- for l + x = 0|
|| 2 2 2 | || 2 2 2 |
|| | || |
|| _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | || _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |
|| / ___________________________________________________________________________________ | || / ___________________________________________________________________________________ |
|| / / ___________________________________________ | || / / ___________________________________________ |
|| / / / 2 | || / / / 2 |
|| / / / / / 4\\ | || / / / / / 4\\ |
|| / / / | 2 | 3*x || | || / / / | 2 | 3*x || |
|| / / / | 6 x *|-l - x - ----|| / 4\ | || / / / | 6 x *|-l - x - ----|| / 4\ |
|| / / / | 3*x \ 16 /| 2 | 3*x | | || / / / | 3*x \ 16 /| 2 | 3*x | |
y1 = I*im|< / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| 3 | + re|< / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| 3 |
|| / / / \ 32 2 / (l + x) 3*x \ 16 / 2 2*x 2*(l + x) | || / / / \ 32 2 / (l + x) 3*x \ 16 / 2 2*x 2*(l + x) |
|| / - 2*3 / / ------------------------------ + -------- + ---- + ------------------ + 2*x + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------ | || / - 2*3 / / ------------------------------ + -------- + ---- + ------------------ + 2*x + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------ |
|| __________________________________________________________________________________________________________________________________________________________________________________________________________ / \/ \/ 4 27 64 4 __________________________________________________________________________________________________________________________________________________________________________________________________________ ___________________________________________________________________________________ | || __________________________________________________________________________________________________________________________________________________________________________________________________________ / \/ \/ 4 27 64 4 __________________________________________________________________________________________________________________________________________________________________________________________________________ ___________________________________________________________________________________ |
|| / ___________________________________________________________________________________ / / ___________________________________________________________________________________ / ___________________________________________ | || / ___________________________________________________________________________________ / / ___________________________________________________________________________________ / ___________________________________________ |
|| / / ___________________________________________ / / / ___________________________________________ / / 2 | || / / ___________________________________________ / / / ___________________________________________ / / 2 |
|| / / / 2 / / / / 2 / / / / 4\\ | || / / / 2 / / / / 2 / / / / 4\\ |
|| / / / / / 4\\ / / / / / / 4\\ / / | 2 | 3*x || | || / / / / / 4\\ / / / / / / 4\\ / / | 2 | 3*x || |
|| / / / | 2 | 3*x || / / / / | 2 | 3*x || / / | 6 x *|-l - x - ----|| / 4\ | || / / / | 2 | 3*x || / / / / | 2 | 3*x || / / | 6 x *|-l - x - ----|| / 4\ |
|| / / / | 6 x *|-l - x - ----|| / 4\ / / / / | 6 x *|-l - x - ----|| / 4\ / / | 3*x \ 16 /| 2 | 3*x | | || / / / | 6 x *|-l - x - ----|| / 4\ / / / / | 6 x *|-l - x - ----|| / 4\ / / | 3*x \ 16 /| 2 | 3*x | |
|| / / / | 3*x \ 16 /| 2 | 3*x | / / / / | 3*x \ 16 /| 2 | 3*x | / / |- ---- - ------------------| 3 6 x *|-l - x - ----| | || / / / | 3*x \ 16 /| 2 | 3*x | / / / / | 3*x \ 16 /| 2 | 3*x | / / |- ---- - ------------------| 3 6 x *|-l - x - ----| |
|| / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| / / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| / / \ 32 2 / (l + x) 3*x \ 16 / | || / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| / / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| / / \ 32 2 / (l + x) 3*x \ 16 / |
|| / 2 / / \ 32 2 / (l + x) 3*x \ 16 / 2*(l + x) / / 2 / / \ 32 2 / (l + x) 3*x \ 16 / 2*(l + x) 3*3 / / ------------------------------ + -------- + ---- + ------------------ | || / 2 / / \ 32 2 / (l + x) 3*x \ 16 / 2*(l + x) / / 2 / / \ 32 2 / (l + x) 3*x \ 16 / 2*(l + x) 3*3 / / ------------------------------ + -------- + ---- + ------------------ |
|| / x + 2*3 / / ------------------------------ + -------- + ---- + ------------------ - ------------------------------------------------------------------------------------------------ / / x + 2*3 / / ------------------------------ + -------- + ---- + ------------------ - ------------------------------------------------------------------------------------------------ \/ \/ 4 27 64 4 | || / x + 2*3 / / ------------------------------ + -------- + ---- + ------------------ - ------------------------------------------------------------------------------------------------ / / x + 2*3 / / ------------------------------ + -------- + ---- + ------------------ - ------------------------------------------------------------------------------------------------ \/ \/ 4 27 64 4 |
|| / \/ \/ 4 27 64 4 ___________________________________________________________________________________ / / \/ \/ 4 27 64 4 ___________________________________________________________________________________ | || / \/ \/ 4 27 64 4 ___________________________________________________________________________________ / / \/ \/ 4 27 64 4 ___________________________________________________________________________________ |
|| / / ___________________________________________ / / / ___________________________________________ | || / / ___________________________________________ / / / ___________________________________________ |
|| / / / 2 / / / / 2 | || / / / 2 / / / / 2 |
|| / / / / / 4\\ / / / / / / 4\\ | || / / / / / 4\\ / / / / / / 4\\ |
|| / / / | 2 | 3*x || / / / / | 2 | 3*x || | || / / / | 2 | 3*x || / / / / | 2 | 3*x || |
|| / / / | 6 x *|-l - x - ----|| / 4\ / / / / | 6 x *|-l - x - ----|| / 4\ | || / / / | 6 x *|-l - x - ----|| / 4\ / / / / | 6 x *|-l - x - ----|| / 4\ |
|| / / / | 3*x \ 16 /| 2 | 3*x | / / / / | 3*x \ 16 /| 2 | 3*x | | || / / / | 3*x \ 16 /| 2 | 3*x | / / / / | 3*x \ 16 /| 2 | 3*x | |
|| / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| / / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| | || / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| / / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| |
|| / / / \ 32 2 / (l + x) 3*x \ 16 / / / / / \ 32 2 / (l + x) 3*x \ 16 / | || / / / \ 32 2 / (l + x) 3*x \ 16 / / / / / \ 32 2 / (l + x) 3*x \ 16 / |
|| / 3*3 / / ------------------------------ + -------- + ---- + ------------------ / / 3*3 / / ------------------------------ + -------- + ---- + ------------------ | || / 3*3 / / ------------------------------ + -------- + ---- + ------------------ / / 3*3 / / ------------------------------ + -------- + ---- + ------------------ |
|| x \/ \/ \/ 4 27 64 4 \/ \/ \/ \/ 4 27 64 4 | || x \/ \/ \/ 4 27 64 4 \/ \/ \/ \/ 4 27 64 4 |
||- - - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise | ||- - - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise |
\\ 2 2 2 / \\ 2 2 2 /
$$y_{1} = \operatorname{re}{\left(\begin{cases} - \frac{x}{2} - \frac{\sqrt{x^{2} - 2 \sqrt[3]{- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}}}}{2} - \frac{\sqrt{\frac{2 x^{3}}{\sqrt{x^{2} - 2 \sqrt[3]{- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}}}} + 2 x^{2} + 2 \sqrt[3]{- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}}}}{2} & \text{for}\: l + x = 0 \\- \frac{x}{2} - \frac{\sqrt{x^{2} - \frac{2 \left(l + x\right)}{3 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}}}{2} - \frac{\sqrt{\frac{2 x^{3}}{\sqrt{x^{2} - \frac{2 \left(l + x\right)}{3 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}}} + 2 x^{2} + \frac{2 \left(l + x\right)}{3 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}} - 2 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}}}{2} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{x}{2} - \frac{\sqrt{x^{2} - 2 \sqrt[3]{- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}}}}{2} - \frac{\sqrt{\frac{2 x^{3}}{\sqrt{x^{2} - 2 \sqrt[3]{- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}}}} + 2 x^{2} + 2 \sqrt[3]{- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}}}}{2} & \text{for}\: l + x = 0 \\- \frac{x}{2} - \frac{\sqrt{x^{2} - \frac{2 \left(l + x\right)}{3 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}}}{2} - \frac{\sqrt{\frac{2 x^{3}}{\sqrt{x^{2} - \frac{2 \left(l + x\right)}{3 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}}} + 2 x^{2} + \frac{2 \left(l + x\right)}{3 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}} - 2 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}}}{2} & \text{otherwise} \end{cases}\right)}$$
// _______________________________________________________________________________________________________ \ // _______________________________________________________________________________________________________ \
|| / _____________________________ | || / _____________________________ |
|| / / / 4\ | || / / / 4\ |
|| / / 2 | 3*x | | || / / 2 | 3*x | |
|| / / 6 x *|-l - x - ----| 3 | || / / 6 x *|-l - x - ----| 3 |
|| / 2 / 3*x \ 16 / 2*x | || / 2 / 3*x \ 16 / 2*x |
|| / 2*x + 2*3 / - ---- - ------------------ + ----------------------------------------------------- | || / 2*x + 2*3 / - ---- - ------------------ + ----------------------------------------------------- |
|| / \/ 32 2 _____________________________________________ _____________________________________________ | || / \/ 32 2 _____________________________________________ _____________________________________________ |
|| / / _____________________________ / _____________________________ | || / / _____________________________ / _____________________________ |
|| / / / / 4\ / / / 4\ | || / / / / 4\ / / / 4\ |
|| / / / 2 | 3*x | / / 2 | 3*x | | || / / / 2 | 3*x | / / 2 | 3*x | |
|| / / / 6 x *|-l - x - ----| / / 6 x *|-l - x - ----| | || / / / 6 x *|-l - x - ----| / / 6 x *|-l - x - ----| |
|| / / 2 / 3*x \ 16 / / 2 / 3*x \ 16 / | || / / 2 / 3*x \ 16 / / 2 / 3*x \ 16 / |
|| / / x - 2*3 / - ---- - ------------------ / x - 2*3 / - ---- - ------------------ | || / / x - 2*3 / - ---- - ------------------ / x - 2*3 / - ---- - ------------------ |
|| \/ \/ \/ 32 2 x \/ \/ 32 2 | || \/ \/ \/ 32 2 x \/ \/ 32 2 |
|| ---------------------------------------------------------------------------------------------------------------------- - - - ----------------------------------------------------- for l + x = 0| || ---------------------------------------------------------------------------------------------------------------------- - - - ----------------------------------------------------- for l + x = 0|
|| 2 2 2 | || 2 2 2 |
|| | || |
|| _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | || _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |
|| / ___________________________________________________________________________________ | || / ___________________________________________________________________________________ |
|| / / ___________________________________________ | || / / ___________________________________________ |
|| / / / 2 | || / / / 2 |
|| / / / / / 4\\ | || / / / / / 4\\ |
|| / / / | 2 | 3*x || | || / / / | 2 | 3*x || |
|| / / / | 6 x *|-l - x - ----|| / 4\ | || / / / | 6 x *|-l - x - ----|| / 4\ |
|| / / / | 3*x \ 16 /| 2 | 3*x | | || / / / | 3*x \ 16 /| 2 | 3*x | |
y2 = I*im|< / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| 3 | + re|< / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| 3 |
|| / / / \ 32 2 / (l + x) 3*x \ 16 / 2 2*x 2*(l + x) | || / / / \ 32 2 / (l + x) 3*x \ 16 / 2 2*x 2*(l + x) |
|| / - 2*3 / / ------------------------------ + -------- + ---- + ------------------ + 2*x + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------ | || / - 2*3 / / ------------------------------ + -------- + ---- + ------------------ + 2*x + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------ |
|| / \/ \/ 4 27 64 4 __________________________________________________________________________________________________________________________________________________________________________________________________________ ___________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________________________________________________________________ | || / \/ \/ 4 27 64 4 __________________________________________________________________________________________________________________________________________________________________________________________________________ ___________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________________________________________________________________ |
|| / / ___________________________________________________________________________________ / ___________________________________________ / ___________________________________________________________________________________ | || / / ___________________________________________________________________________________ / ___________________________________________ / ___________________________________________________________________________________ |
|| / / / ___________________________________________ / / 2 / / ___________________________________________ | || / / / ___________________________________________ / / 2 / / ___________________________________________ |
|| / / / / 2 / / / / 4\\ / / / 2 | || / / / / 2 / / / / 4\\ / / / 2 |
|| / / / / / / 4\\ / / | 2 | 3*x || / / / / / 4\\ | || / / / / / / 4\\ / / | 2 | 3*x || / / / / / 4\\ |
|| / / / / | 2 | 3*x || / / | 6 x *|-l - x - ----|| / 4\ / / / | 2 | 3*x || | || / / / / | 2 | 3*x || / / | 6 x *|-l - x - ----|| / 4\ / / / | 2 | 3*x || |
|| / / / / | 6 x *|-l - x - ----|| / 4\ / / | 3*x \ 16 /| 2 | 3*x | / / / | 6 x *|-l - x - ----|| / 4\ | || / / / / | 6 x *|-l - x - ----|| / 4\ / / | 3*x \ 16 /| 2 | 3*x | / / / | 6 x *|-l - x - ----|| / 4\ |
|| / / / / | 3*x \ 16 /| 2 | 3*x | / / |- ---- - ------------------| 3 6 x *|-l - x - ----| / / / | 3*x \ 16 /| 2 | 3*x | | || / / / / | 3*x \ 16 /| 2 | 3*x | / / |- ---- - ------------------| 3 6 x *|-l - x - ----| / / / | 3*x \ 16 /| 2 | 3*x | |
|| / / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| / / \ 32 2 / (l + x) 3*x \ 16 / / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| | || / / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| / / \ 32 2 / (l + x) 3*x \ 16 / / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| |
|| / / 2 / / \ 32 2 / (l + x) 3*x \ 16 / 2*(l + x) 3*3 / / ------------------------------ + -------- + ---- + ------------------ / 2 / / \ 32 2 / (l + x) 3*x \ 16 / 2*(l + x) | || / / 2 / / \ 32 2 / (l + x) 3*x \ 16 / 2*(l + x) 3*3 / / ------------------------------ + -------- + ---- + ------------------ / 2 / / \ 32 2 / (l + x) 3*x \ 16 / 2*(l + x) |
|| / / x + 2*3 / / ------------------------------ + -------- + ---- + ------------------ - ------------------------------------------------------------------------------------------------ \/ \/ 4 27 64 4 / x + 2*3 / / ------------------------------ + -------- + ---- + ------------------ - ------------------------------------------------------------------------------------------------ | || / / x + 2*3 / / ------------------------------ + -------- + ---- + ------------------ - ------------------------------------------------------------------------------------------------ \/ \/ 4 27 64 4 / x + 2*3 / / ------------------------------ + -------- + ---- + ------------------ - ------------------------------------------------------------------------------------------------ |
|| / / \/ \/ 4 27 64 4 ___________________________________________________________________________________ / \/ \/ 4 27 64 4 ___________________________________________________________________________________ | || / / \/ \/ 4 27 64 4 ___________________________________________________________________________________ / \/ \/ 4 27 64 4 ___________________________________________________________________________________ |
|| / / / ___________________________________________ / / ___________________________________________ | || / / / ___________________________________________ / / ___________________________________________ |
|| / / / / 2 / / / 2 | || / / / / 2 / / / 2 |
|| / / / / / / 4\\ / / / / / 4\\ | || / / / / / / 4\\ / / / / / 4\\ |
|| / / / / | 2 | 3*x || / / / | 2 | 3*x || | || / / / / | 2 | 3*x || / / / | 2 | 3*x || |
|| / / / / | 6 x *|-l - x - ----|| / 4\ / / / | 6 x *|-l - x - ----|| / 4\ | || / / / / | 6 x *|-l - x - ----|| / 4\ / / / | 6 x *|-l - x - ----|| / 4\ |
|| / / / / | 3*x \ 16 /| 2 | 3*x | / / / | 3*x \ 16 /| 2 | 3*x | | || / / / / | 3*x \ 16 /| 2 | 3*x | / / / | 3*x \ 16 /| 2 | 3*x | |
|| / / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| | || / / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| |
|| / / / / \ 32 2 / (l + x) 3*x \ 16 / / / / \ 32 2 / (l + x) 3*x \ 16 / | || / / / / \ 32 2 / (l + x) 3*x \ 16 / / / / \ 32 2 / (l + x) 3*x \ 16 / |
|| / / 3*3 / / ------------------------------ + -------- + ---- + ------------------ / 3*3 / / ------------------------------ + -------- + ---- + ------------------ | || / / 3*3 / / ------------------------------ + -------- + ---- + ------------------ / 3*3 / / ------------------------------ + -------- + ---- + ------------------ |
||\/ \/ \/ \/ 4 27 64 4 x \/ \/ \/ 4 27 64 4 | ||\/ \/ \/ \/ 4 27 64 4 x \/ \/ \/ 4 27 64 4 |
||---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - - - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise | ||---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - - - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise |
\\ 2 2 2 / \\ 2 2 2 /
$$y_{2} = \operatorname{re}{\left(\begin{cases} - \frac{x}{2} - \frac{\sqrt{x^{2} - 2 \sqrt[3]{- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}}}}{2} + \frac{\sqrt{\frac{2 x^{3}}{\sqrt{x^{2} - 2 \sqrt[3]{- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}}}} + 2 x^{2} + 2 \sqrt[3]{- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}}}}{2} & \text{for}\: l + x = 0 \\- \frac{x}{2} - \frac{\sqrt{x^{2} - \frac{2 \left(l + x\right)}{3 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}}}{2} + \frac{\sqrt{\frac{2 x^{3}}{\sqrt{x^{2} - \frac{2 \left(l + x\right)}{3 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}}} + 2 x^{2} + \frac{2 \left(l + x\right)}{3 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}} - 2 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}}}{2} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{x}{2} - \frac{\sqrt{x^{2} - 2 \sqrt[3]{- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}}}}{2} + \frac{\sqrt{\frac{2 x^{3}}{\sqrt{x^{2} - 2 \sqrt[3]{- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}}}} + 2 x^{2} + 2 \sqrt[3]{- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}}}}{2} & \text{for}\: l + x = 0 \\- \frac{x}{2} - \frac{\sqrt{x^{2} - \frac{2 \left(l + x\right)}{3 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}}}{2} + \frac{\sqrt{\frac{2 x^{3}}{\sqrt{x^{2} - \frac{2 \left(l + x\right)}{3 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}}} + 2 x^{2} + \frac{2 \left(l + x\right)}{3 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}} - 2 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}}}{2} & \text{otherwise} \end{cases}\right)}$$
// _______________________________________________________________________________________________________ \ // _______________________________________________________________________________________________________ \
|| / _____________________________ | || / _____________________________ |
|| / / / 4\ | || / / / 4\ |
|| / / 2 | 3*x | | || / / 2 | 3*x | |
|| / / 6 x *|-l - x - ----| 3 | || / / 6 x *|-l - x - ----| 3 |
|| / 2 / 3*x \ 16 / 2*x | || / 2 / 3*x \ 16 / 2*x |
|| / 2*x + 2*3 / - ---- - ------------------ - ----------------------------------------------------- | || / 2*x + 2*3 / - ---- - ------------------ - ----------------------------------------------------- |
|| _____________________________________________ / \/ 32 2 _____________________________________________ | || _____________________________________________ / \/ 32 2 _____________________________________________ |
|| / _____________________________ / / _____________________________ | || / _____________________________ / / _____________________________ |
|| / / / 4\ / / / / 4\ | || / / / 4\ / / / / 4\ |
|| / / 2 | 3*x | / / / 2 | 3*x | | || / / 2 | 3*x | / / / 2 | 3*x | |
|| / / 6 x *|-l - x - ----| / / / 6 x *|-l - x - ----| | || / / 6 x *|-l - x - ----| / / / 6 x *|-l - x - ----| |
|| / 2 / 3*x \ 16 / / / 2 / 3*x \ 16 / | || / 2 / 3*x \ 16 / / / 2 / 3*x \ 16 / |
|| / x - 2*3 / - ---- - ------------------ / / x - 2*3 / - ---- - ------------------ | || / x - 2*3 / - ---- - ------------------ / / x - 2*3 / - ---- - ------------------ |
|| \/ \/ 32 2 x \/ \/ \/ 32 2 | || \/ \/ 32 2 x \/ \/ \/ 32 2 |
|| ----------------------------------------------------- - - - ---------------------------------------------------------------------------------------------------------------------- for l + x = 0| || ----------------------------------------------------- - - - ---------------------------------------------------------------------------------------------------------------------- for l + x = 0|
|| 2 2 2 | || 2 2 2 |
|| | || |
|| _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | || _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |
|| / ___________________________________________________________________________________ | || / ___________________________________________________________________________________ |
|| / / ___________________________________________ | || / / ___________________________________________ |
|| / / / 2 | || / / / 2 |
|| / / / / / 4\\ | || / / / / / 4\\ |
|| / / / | 2 | 3*x || | || / / / | 2 | 3*x || |
|| / / / | 6 x *|-l - x - ----|| / 4\ | || / / / | 6 x *|-l - x - ----|| / 4\ |
|| / / / | 3*x \ 16 /| 2 | 3*x | | || / / / | 3*x \ 16 /| 2 | 3*x | |
y3 = I*im|< / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| 3 | + re|< / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| 3 |
|| / / / \ 32 2 / (l + x) 3*x \ 16 / 2 2*x 2*(l + x) | || / / / \ 32 2 / (l + x) 3*x \ 16 / 2 2*x 2*(l + x) |
|| / - 2*3 / / ------------------------------ + -------- + ---- + ------------------ + 2*x - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------ | || / - 2*3 / / ------------------------------ + -------- + ---- + ------------------ + 2*x - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------ |
|| __________________________________________________________________________________________________________________________________________________________________________________________________________ / \/ \/ 4 27 64 4 __________________________________________________________________________________________________________________________________________________________________________________________________________ ___________________________________________________________________________________ | || __________________________________________________________________________________________________________________________________________________________________________________________________________ / \/ \/ 4 27 64 4 __________________________________________________________________________________________________________________________________________________________________________________________________________ ___________________________________________________________________________________ |
|| / ___________________________________________________________________________________ / / ___________________________________________________________________________________ / ___________________________________________ | || / ___________________________________________________________________________________ / / ___________________________________________________________________________________ / ___________________________________________ |
|| / / ___________________________________________ / / / ___________________________________________ / / 2 | || / / ___________________________________________ / / / ___________________________________________ / / 2 |
|| / / / 2 / / / / 2 / / / / 4\\ | || / / / 2 / / / / 2 / / / / 4\\ |
|| / / / / / 4\\ / / / / / / 4\\ / / | 2 | 3*x || | || / / / / / 4\\ / / / / / / 4\\ / / | 2 | 3*x || |
|| / / / | 2 | 3*x || / / / / | 2 | 3*x || / / | 6 x *|-l - x - ----|| / 4\ | || / / / | 2 | 3*x || / / / / | 2 | 3*x || / / | 6 x *|-l - x - ----|| / 4\ |
|| / / / | 6 x *|-l - x - ----|| / 4\ / / / / | 6 x *|-l - x - ----|| / 4\ / / | 3*x \ 16 /| 2 | 3*x | | || / / / | 6 x *|-l - x - ----|| / 4\ / / / / | 6 x *|-l - x - ----|| / 4\ / / | 3*x \ 16 /| 2 | 3*x | |
|| / / / | 3*x \ 16 /| 2 | 3*x | / / / / | 3*x \ 16 /| 2 | 3*x | / / |- ---- - ------------------| 3 6 x *|-l - x - ----| | || / / / | 3*x \ 16 /| 2 | 3*x | / / / / | 3*x \ 16 /| 2 | 3*x | / / |- ---- - ------------------| 3 6 x *|-l - x - ----| |
|| / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| / / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| / / \ 32 2 / (l + x) 3*x \ 16 / | || / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| / / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| / / \ 32 2 / (l + x) 3*x \ 16 / |
|| / 2 / / \ 32 2 / (l + x) 3*x \ 16 / 2*(l + x) / / 2 / / \ 32 2 / (l + x) 3*x \ 16 / 2*(l + x) 3*3 / / ------------------------------ + -------- + ---- + ------------------ | || / 2 / / \ 32 2 / (l + x) 3*x \ 16 / 2*(l + x) / / 2 / / \ 32 2 / (l + x) 3*x \ 16 / 2*(l + x) 3*3 / / ------------------------------ + -------- + ---- + ------------------ |
|| / x + 2*3 / / ------------------------------ + -------- + ---- + ------------------ - ------------------------------------------------------------------------------------------------ / / x + 2*3 / / ------------------------------ + -------- + ---- + ------------------ - ------------------------------------------------------------------------------------------------ \/ \/ 4 27 64 4 | || / x + 2*3 / / ------------------------------ + -------- + ---- + ------------------ - ------------------------------------------------------------------------------------------------ / / x + 2*3 / / ------------------------------ + -------- + ---- + ------------------ - ------------------------------------------------------------------------------------------------ \/ \/ 4 27 64 4 |
|| / \/ \/ 4 27 64 4 ___________________________________________________________________________________ / / \/ \/ 4 27 64 4 ___________________________________________________________________________________ | || / \/ \/ 4 27 64 4 ___________________________________________________________________________________ / / \/ \/ 4 27 64 4 ___________________________________________________________________________________ |
|| / / ___________________________________________ / / / ___________________________________________ | || / / ___________________________________________ / / / ___________________________________________ |
|| / / / 2 / / / / 2 | || / / / 2 / / / / 2 |
|| / / / / / 4\\ / / / / / / 4\\ | || / / / / / 4\\ / / / / / / 4\\ |
|| / / / | 2 | 3*x || / / / / | 2 | 3*x || | || / / / | 2 | 3*x || / / / / | 2 | 3*x || |
|| / / / | 6 x *|-l - x - ----|| / 4\ / / / / | 6 x *|-l - x - ----|| / 4\ | || / / / | 6 x *|-l - x - ----|| / 4\ / / / / | 6 x *|-l - x - ----|| / 4\ |
|| / / / | 3*x \ 16 /| 2 | 3*x | / / / / | 3*x \ 16 /| 2 | 3*x | | || / / / | 3*x \ 16 /| 2 | 3*x | / / / / | 3*x \ 16 /| 2 | 3*x | |
|| / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| / / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| | || / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| / / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| |
|| / / / \ 32 2 / (l + x) 3*x \ 16 / / / / / \ 32 2 / (l + x) 3*x \ 16 / | || / / / \ 32 2 / (l + x) 3*x \ 16 / / / / / \ 32 2 / (l + x) 3*x \ 16 / |
|| / 3*3 / / ------------------------------ + -------- + ---- + ------------------ / / 3*3 / / ------------------------------ + -------- + ---- + ------------------ | || / 3*3 / / ------------------------------ + -------- + ---- + ------------------ / / 3*3 / / ------------------------------ + -------- + ---- + ------------------ |
||\/ \/ \/ 4 27 64 4 x \/ \/ \/ \/ 4 27 64 4 | ||\/ \/ \/ 4 27 64 4 x \/ \/ \/ \/ 4 27 64 4 |
||-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - - - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise | ||-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - - - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- otherwise |
\\ 2 2 2 / \\ 2 2 2 /
$$y_{3} = \operatorname{re}{\left(\begin{cases} - \frac{x}{2} + \frac{\sqrt{x^{2} - 2 \sqrt[3]{- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}}}}{2} - \frac{\sqrt{- \frac{2 x^{3}}{\sqrt{x^{2} - 2 \sqrt[3]{- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}}}} + 2 x^{2} + 2 \sqrt[3]{- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}}}}{2} & \text{for}\: l + x = 0 \\- \frac{x}{2} + \frac{\sqrt{x^{2} - \frac{2 \left(l + x\right)}{3 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}}}{2} - \frac{\sqrt{- \frac{2 x^{3}}{\sqrt{x^{2} - \frac{2 \left(l + x\right)}{3 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}}} + 2 x^{2} + \frac{2 \left(l + x\right)}{3 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}} - 2 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}}}{2} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{x}{2} + \frac{\sqrt{x^{2} - 2 \sqrt[3]{- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}}}}{2} - \frac{\sqrt{- \frac{2 x^{3}}{\sqrt{x^{2} - 2 \sqrt[3]{- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}}}} + 2 x^{2} + 2 \sqrt[3]{- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}}}}{2} & \text{for}\: l + x = 0 \\- \frac{x}{2} + \frac{\sqrt{x^{2} - \frac{2 \left(l + x\right)}{3 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}}}{2} - \frac{\sqrt{- \frac{2 x^{3}}{\sqrt{x^{2} - \frac{2 \left(l + x\right)}{3 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}}} + 2 x^{2} + \frac{2 \left(l + x\right)}{3 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}} - 2 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}}}{2} & \text{otherwise} \end{cases}\right)}$$
// _______________________________________________________________________________________________________ \ // _______________________________________________________________________________________________________ \
|| / _____________________________ | || / _____________________________ |
|| / / / 4\ | || / / / 4\ |
|| / / 2 | 3*x | | || / / 2 | 3*x | |
|| / / 6 x *|-l - x - ----| 3 | || / / 6 x *|-l - x - ----| 3 |
|| / 2 / 3*x \ 16 / 2*x | || / 2 / 3*x \ 16 / 2*x |
|| / 2*x + 2*3 / - ---- - ------------------ - ----------------------------------------------------- | || / 2*x + 2*3 / - ---- - ------------------ - ----------------------------------------------------- |
|| _____________________________________________ / \/ 32 2 _____________________________________________ | || _____________________________________________ / \/ 32 2 _____________________________________________ |
|| / _____________________________ / / _____________________________ | || / _____________________________ / / _____________________________ |
|| / / / 4\ / / / / 4\ | || / / / 4\ / / / / 4\ |
|| / / 2 | 3*x | / / / 2 | 3*x | | || / / 2 | 3*x | / / / 2 | 3*x | |
|| / / 6 x *|-l - x - ----| / / / 6 x *|-l - x - ----| | || / / 6 x *|-l - x - ----| / / / 6 x *|-l - x - ----| |
|| / 2 / 3*x \ 16 / / / 2 / 3*x \ 16 / | || / 2 / 3*x \ 16 / / / 2 / 3*x \ 16 / |
|| / x - 2*3 / - ---- - ------------------ / / x - 2*3 / - ---- - ------------------ | || / x - 2*3 / - ---- - ------------------ / / x - 2*3 / - ---- - ------------------ |
|| \/ \/ 32 2 \/ \/ \/ 32 2 x | || \/ \/ 32 2 \/ \/ \/ 32 2 x |
|| ----------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------- - - for l + x = 0| || ----------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------- - - for l + x = 0|
|| 2 2 2 | || 2 2 2 |
|| | || |
|| _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | || _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |
|| / ___________________________________________________________________________________ | || / ___________________________________________________________________________________ |
|| / / ___________________________________________ | || / / ___________________________________________ |
|| / / / 2 | || / / / 2 |
|| / / / / / 4\\ | || / / / / / 4\\ |
|| / / / | 2 | 3*x || | || / / / | 2 | 3*x || |
|| / / / | 6 x *|-l - x - ----|| / 4\ | || / / / | 6 x *|-l - x - ----|| / 4\ |
|| / / / | 3*x \ 16 /| 2 | 3*x | | || / / / | 3*x \ 16 /| 2 | 3*x | |
y4 = I*im|< / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| 3 | + re|< / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| 3 |
|| / / / \ 32 2 / (l + x) 3*x \ 16 / 2 2*x 2*(l + x) | || / / / \ 32 2 / (l + x) 3*x \ 16 / 2 2*x 2*(l + x) |
|| / - 2*3 / / ------------------------------ + -------- + ---- + ------------------ + 2*x - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------ | || / - 2*3 / / ------------------------------ + -------- + ---- + ------------------ + 2*x - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------ |
|| __________________________________________________________________________________________________________________________________________________________________________________________________________ / \/ \/ 4 27 64 4 __________________________________________________________________________________________________________________________________________________________________________________________________________ ___________________________________________________________________________________ | || __________________________________________________________________________________________________________________________________________________________________________________________________________ / \/ \/ 4 27 64 4 __________________________________________________________________________________________________________________________________________________________________________________________________________ ___________________________________________________________________________________ |
|| / ___________________________________________________________________________________ / / ___________________________________________________________________________________ / ___________________________________________ | || / ___________________________________________________________________________________ / / ___________________________________________________________________________________ / ___________________________________________ |
|| / / ___________________________________________ / / / ___________________________________________ / / 2 | || / / ___________________________________________ / / / ___________________________________________ / / 2 |
|| / / / 2 / / / / 2 / / / / 4\\ | || / / / 2 / / / / 2 / / / / 4\\ |
|| / / / / / 4\\ / / / / / / 4\\ / / | 2 | 3*x || | || / / / / / 4\\ / / / / / / 4\\ / / | 2 | 3*x || |
|| / / / | 2 | 3*x || / / / / | 2 | 3*x || / / | 6 x *|-l - x - ----|| / 4\ | || / / / | 2 | 3*x || / / / / | 2 | 3*x || / / | 6 x *|-l - x - ----|| / 4\ |
|| / / / | 6 x *|-l - x - ----|| / 4\ / / / / | 6 x *|-l - x - ----|| / 4\ / / | 3*x \ 16 /| 2 | 3*x | | || / / / | 6 x *|-l - x - ----|| / 4\ / / / / | 6 x *|-l - x - ----|| / 4\ / / | 3*x \ 16 /| 2 | 3*x | |
|| / / / | 3*x \ 16 /| 2 | 3*x | / / / / | 3*x \ 16 /| 2 | 3*x | / / |- ---- - ------------------| 3 6 x *|-l - x - ----| | || / / / | 3*x \ 16 /| 2 | 3*x | / / / / | 3*x \ 16 /| 2 | 3*x | / / |- ---- - ------------------| 3 6 x *|-l - x - ----| |
|| / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| / / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| / / \ 32 2 / (l + x) 3*x \ 16 / | || / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| / / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| / / \ 32 2 / (l + x) 3*x \ 16 / |
|| / 2 / / \ 32 2 / (l + x) 3*x \ 16 / 2*(l + x) / / 2 / / \ 32 2 / (l + x) 3*x \ 16 / 2*(l + x) 3*3 / / ------------------------------ + -------- + ---- + ------------------ | || / 2 / / \ 32 2 / (l + x) 3*x \ 16 / 2*(l + x) / / 2 / / \ 32 2 / (l + x) 3*x \ 16 / 2*(l + x) 3*3 / / ------------------------------ + -------- + ---- + ------------------ |
|| / x + 2*3 / / ------------------------------ + -------- + ---- + ------------------ - ------------------------------------------------------------------------------------------------ / / x + 2*3 / / ------------------------------ + -------- + ---- + ------------------ - ------------------------------------------------------------------------------------------------ \/ \/ 4 27 64 4 | || / x + 2*3 / / ------------------------------ + -------- + ---- + ------------------ - ------------------------------------------------------------------------------------------------ / / x + 2*3 / / ------------------------------ + -------- + ---- + ------------------ - ------------------------------------------------------------------------------------------------ \/ \/ 4 27 64 4 |
|| / \/ \/ 4 27 64 4 ___________________________________________________________________________________ / / \/ \/ 4 27 64 4 ___________________________________________________________________________________ | || / \/ \/ 4 27 64 4 ___________________________________________________________________________________ / / \/ \/ 4 27 64 4 ___________________________________________________________________________________ |
|| / / ___________________________________________ / / / ___________________________________________ | || / / ___________________________________________ / / / ___________________________________________ |
|| / / / 2 / / / / 2 | || / / / 2 / / / / 2 |
|| / / / / / 4\\ / / / / / / 4\\ | || / / / / / 4\\ / / / / / / 4\\ |
|| / / / | 2 | 3*x || / / / / | 2 | 3*x || | || / / / | 2 | 3*x || / / / / | 2 | 3*x || |
|| / / / | 6 x *|-l - x - ----|| / 4\ / / / / | 6 x *|-l - x - ----|| / 4\ | || / / / | 6 x *|-l - x - ----|| / 4\ / / / / | 6 x *|-l - x - ----|| / 4\ |
|| / / / | 3*x \ 16 /| 2 | 3*x | / / / / | 3*x \ 16 /| 2 | 3*x | | || / / / | 3*x \ 16 /| 2 | 3*x | / / / / | 3*x \ 16 /| 2 | 3*x | |
|| / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| / / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| | || / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| / / / / |- ---- - ------------------| 3 6 x *|-l - x - ----| |
|| / / / \ 32 2 / (l + x) 3*x \ 16 / / / / / \ 32 2 / (l + x) 3*x \ 16 / | || / / / \ 32 2 / (l + x) 3*x \ 16 / / / / / \ 32 2 / (l + x) 3*x \ 16 / |
|| / 3*3 / / ------------------------------ + -------- + ---- + ------------------ / / 3*3 / / ------------------------------ + -------- + ---- + ------------------ | || / 3*3 / / ------------------------------ + -------- + ---- + ------------------ / / 3*3 / / ------------------------------ + -------- + ---- + ------------------ |
||\/ \/ \/ 4 27 64 4 \/ \/ \/ \/ 4 27 64 4 x | ||\/ \/ \/ 4 27 64 4 \/ \/ \/ \/ 4 27 64 4 x |
||-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - - otherwise | ||-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - - otherwise |
\\ 2 2 2 / \\ 2 2 2 /
$$y_{4} = \operatorname{re}{\left(\begin{cases} - \frac{x}{2} + \frac{\sqrt{x^{2} - 2 \sqrt[3]{- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}}}}{2} + \frac{\sqrt{- \frac{2 x^{3}}{\sqrt{x^{2} - 2 \sqrt[3]{- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}}}} + 2 x^{2} + 2 \sqrt[3]{- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}}}}{2} & \text{for}\: l + x = 0 \\- \frac{x}{2} + \frac{\sqrt{x^{2} - \frac{2 \left(l + x\right)}{3 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}}}{2} + \frac{\sqrt{- \frac{2 x^{3}}{\sqrt{x^{2} - \frac{2 \left(l + x\right)}{3 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}}} + 2 x^{2} + \frac{2 \left(l + x\right)}{3 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}} - 2 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}}}{2} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{x}{2} + \frac{\sqrt{x^{2} - 2 \sqrt[3]{- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}}}}{2} + \frac{\sqrt{- \frac{2 x^{3}}{\sqrt{x^{2} - 2 \sqrt[3]{- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}}}} + 2 x^{2} + 2 \sqrt[3]{- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}}}}{2} & \text{for}\: l + x = 0 \\- \frac{x}{2} + \frac{\sqrt{x^{2} - \frac{2 \left(l + x\right)}{3 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}}}{2} + \frac{\sqrt{- \frac{2 x^{3}}{\sqrt{x^{2} - \frac{2 \left(l + x\right)}{3 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}}} + 2 x^{2} + \frac{2 \left(l + x\right)}{3 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}} - 2 \sqrt[3]{\frac{3 x^{6}}{64} + \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{4} + \sqrt{\frac{\left(l + x\right)^{3}}{27} + \frac{\left(- \frac{3 x^{6}}{32} - \frac{x^{2} \left(- l - \frac{3 x^{4}}{16} - x\right)}{2}\right)^{2}}{4}}}}}{2} & \text{otherwise} \end{cases}\right)}$$
y4 = re(Piecewise((-x/2 + sqrt(x^2 - 2*(-3*x^6/32 - x^2*(-l - 3*x^4/16 - x)/2)^(1/3))/2 + sqrt(-2*x^3/sqrt(x^2 - 2*(-3*x^6/32 - x^2*(-l - 3*x^4/16 - x)/2)^(1/3)) + 2*x^2 + 2*(-3*x^6/32 - x^2*(-l - 3*x^4/16 - x)/2)^(1/3)/2, l + x = 0), (-x/2 + sqrt(x^2 - 2*(l + x)/(3*(3*x^6/64 + x^2*(-l - 3*x^4/16 - x)/4 + sqrt((l + x)^3/27 + (-3*x^6/32 - x^2*(-l - 3*x^4/16 - x)/2)^2/4))^(1/3)) + 2*(3*x^6/64 + x^2*(-l - 3*x^4/16 - x)/4 + sqrt((l + x)^3/27 + (-3*x^6/32 - x^2*(-l - 3*x^4/16 - x)/2)^2/4))^(1/3))/2 + sqrt(-2*x^3/sqrt(x^2 - 2*(l + x)/(3*(3*x^6/64 + x^2*(-l - 3*x^4/16 - x)/4 + sqrt((l + x)^3/27 + (-3*x^6/32 - x^2*(-l - 3*x^4/16 - x)/2)^2/4))^(1/3)) + 2*(3*x^6/64 + x^2*(-l - 3*x^4/16 - x)/4 + sqrt((l + x)^3/27 + (-3*x^6/32 - x^2*(-l - 3*x^4/16 - x)/2)^2/4))^(1/3)) + 2*x^2 + 2*(l + x)/(3*(3*x^6/64 + x^2*(-l - 3*x^4/16 - x)/4 + sqrt((l + x)^3/27 + (-3*x^6/32 - x^2*(-l - 3*x^4/16 - x)/2)^2/4))^(1/3)) - 2*(3*x^6/64 + x^2*(-l - 3*x^4/16 - x)/4 + sqrt((l + x)^3/27 + (-3*x^6/32 - x^2*(-l - 3*x^4/16 - x)/2)^2/4))^(1/3))/2, True))) + i*im(Piecewise((-x/2 + sqrt(x^2 - 2*(-3*x^6/32 - x^2*(-l - 3*x^4/16 - x)/2)^(1/3))/2 + sqrt(-2*x^3/sqrt(x^2 - 2*(-3*x^6/32 - x^2*(-l - 3*x^4/16 - x)/2)^(1/3)) + 2*x^2 + 2*(-3*x^6/32 - x^2*(-l - 3*x^4/16 - x)/2)^(1/3))/2, l + x = 0), (-x/2 + sqrt(x^2 - 2*(l + x)/(3*(3*x^6/64 + x^2*(-l - 3*x^4/16 - x)/4 + sqrt((l + x)^3/27 + (-3*x^6/32 - x^2*(-l - 3*x^4/16 - x)/2)^2/4))^(1/3)) + 2*(3*x^6/64 + x^2*(-l - 3*x^4/16 - x)/4 + sqrt((l + x)^3/27 + (-3*x^6/32 - x^2*(-l - 3*x^4/16 - x)/2)^2/4))^(1/3))/2 + sqrt(-2*x^3/sqrt(x^2 - 2*(l + x)/(3*(3*x^6/64 + x^2*(-l - 3*x^4/16 - x)/4 + sqrt((l + x)^3/27 + (-3*x^6/32 - x^2*(-l - 3*x^4/16 - x)/2)^2/4))^(1/3)) + 2*(3*x^6/64 + x^2*(-l - 3*x^4/16 - x)/4 + sqrt((l + x)^3/27 + (-3*x^6/32 - x^2*(-l - 3*x^4/16 - x)/2)^2/4))^(1/3)) + 2*x^2 + 2*(l + x)/(3*(3*x^6/64 + x^2*(-l - 3*x^4/16 - x)/4 + sqrt((l + x)^3/27 + (-3*x^6/32 - x^2*(-l - 3*x^4/16 - x)/2)^2/4))^(1/3)) - 2*(3*x^6/64 + x^2*(-l - 3*x^4/16 - x)/4 + sqrt((l + x)^3/27 + (-3*x^6/32 - x^2*(-l - 3*x^4/16 - x)/2)^2/4))^(1/3))/2, True))))