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y²=x+ln(x/y) la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
 2          /x\
y  = x + log|-|
            \y/
$$y^{2} = x + \log{\left(\frac{x}{y} \right)}$$
Simplificar
Gráfica
Suma y producto de raíces [src] 
suma
    /        /   2  2*x\\     /        /   2  2*x\\
    |       W\2*x *e   /|     |       W\2*x *e   /|
    |   x - ------------|     |   x - ------------|
    |            2      |     |            2      |
I*im\x*e                / + re\x*e                /
$$\operatorname{re}{\left(x e^{x - \frac{W\left(2 x^{2} e^{2 x}\right)}{2}}\right)} + i \operatorname{im}{\left(x e^{x - \frac{W\left(2 x^{2} e^{2 x}\right)}{2}}\right)}$$ 
=
    /        /   2  2*x\\     /        /   2  2*x\\
    |       W\2*x *e   /|     |       W\2*x *e   /|
    |   x - ------------|     |   x - ------------|
    |            2      |     |            2      |
I*im\x*e                / + re\x*e                /
$$\operatorname{re}{\left(x e^{x - \frac{W\left(2 x^{2} e^{2 x}\right)}{2}}\right)} + i \operatorname{im}{\left(x e^{x - \frac{W\left(2 x^{2} e^{2 x}\right)}{2}}\right)}$$ 
producto
    /        /   2  2*x\\     /        /   2  2*x\\
    |       W\2*x *e   /|     |       W\2*x *e   /|
    |   x - ------------|     |   x - ------------|
    |            2      |     |            2      |
I*im\x*e                / + re\x*e                /
$$\operatorname{re}{\left(x e^{x - \frac{W\left(2 x^{2} e^{2 x}\right)}{2}}\right)} + i \operatorname{im}{\left(x e^{x - \frac{W\left(2 x^{2} e^{2 x}\right)}{2}}\right)}$$ 
=
    /        /   2  2*x\\     /        /   2  2*x\\
    |       W\2*x *e   /|     |       W\2*x *e   /|
    |   x - ------------|     |   x - ------------|
    |            2      |     |            2      |
I*im\x*e                / + re\x*e                /
$$\operatorname{re}{\left(x e^{x - \frac{W\left(2 x^{2} e^{2 x}\right)}{2}}\right)} + i \operatorname{im}{\left(x e^{x - \frac{W\left(2 x^{2} e^{2 x}\right)}{2}}\right)}$$ 
i*im(x*exp(x - LambertW(2*x^2*exp(2*x))/2)) + re(x*exp(x - LambertW(2*x^2*exp(2*x))/2))
Respuesta rápida [src] 
         /        /   2  2*x\\     /        /   2  2*x\\
         |       W\2*x *e   /|     |       W\2*x *e   /|
         |   x - ------------|     |   x - ------------|
         |            2      |     |            2      |
y1 = I*im\x*e                / + re\x*e                /
$$y_{1} = \operatorname{re}{\left(x e^{x - \frac{W\left(2 x^{2} e^{2 x}\right)}{2}}\right)} + i \operatorname{im}{\left(x e^{x - \frac{W\left(2 x^{2} e^{2 x}\right)}{2}}\right)}$$ 
y1 = re(x*exp(x - LambertW(2*x^2*exp(2*x))/2)) + i*im(x*exp(x - LambertW(2*x^2*exp(2*x))/2))
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