Sr Examen
Ecuación diferencial x(y^6+1)dx+y^2(x^4+1)dy=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
6 2 d 4 2 d
x + x*y (x) + y (x)*--(y(x)) + x *y (x)*--(y(x)) = 0
dx dx
$$x^{4} y^{2}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + x y^{6}{\left(x \right)} + x + y^{2}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
x^4*y^2*y' + x*y^6 + x + y^2*y' = 0
Respuesta
[src]
______________________
/ / / 2\\
/ | 3*atan\x /| / ___\
3 / tan|C1 - ----------| *\-1 + I*\/ 3 /
\/ \ 2 /
y(x) = ------------------------------------------
2
$$y{\left(x \right)} = \frac{\left(-1 + \sqrt{3} i\right) \sqrt[3]{\tan{\left(C_{1} - \frac{3 \operatorname{atan}{\left(x^{2} \right)}}{2} \right)}}}{2}$$
______________________
/ / / 2\\
/ | 3*atan\x /| / ___\
3 / tan|C1 - ----------| *\-1 - I*\/ 3 /
\/ \ 2 /
y(x) = ------------------------------------------
2
$$y{\left(x \right)} = \frac{\left(-1 - \sqrt{3} i\right) \sqrt[3]{\tan{\left(C_{1} - \frac{3 \operatorname{atan}{\left(x^{2} \right)}}{2} \right)}}}{2}$$
______________________
/ / / 2\\
/ | 3*atan\x /|
y(x) = 3 / tan|C1 - ----------|
\/ \ 2 /
$$y{\left(x \right)} = \sqrt[3]{\tan{\left(C_{1} - \frac{3 \operatorname{atan}{\left(x^{2} \right)}}{2} \right)}}$$
Clasificación
separable
1st power series
lie group
separable Integral