Sr Examen
Ecuación diferencial xdx-ydy=yx^2-xy^2dx
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2
d 2 x *y(x)
x - --(y(x))*y(x) = - x*y (x) + -------
dx dx
$$x - y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = - x y^{2}{\left(x \right)} + \frac{x^{2} y{\left(x \right)}}{dx}$$
x - y*y' = -x*y^2 + x^2*y/dx
Respuesta
[src]
5 / 1 \ 4 / 1 \ / 1 \
2 / 1 \ x *|1 - ---| x *|1 - ---|*|C1 + --|
x *|C1 + --| 3 | 2| | 2| \ C1/
\ C1/ x \ C1 / \ C1 / / 6\
y(x) = C1 + ------------ - ---- - ------------ + ---------------------- + O\x /
2 3*dx 15*dx 8
$$y{\left(x \right)} = - \frac{x^{3}}{3 dx} - \frac{x^{5} \left(1 - \frac{1}{C_{1}^{2}}\right)}{15 dx} + \frac{x^{2} \left(C_{1} + \frac{1}{C_{1}}\right)}{2} + \frac{x^{4} \left(1 - \frac{1}{C_{1}^{2}}\right) \left(C_{1} + \frac{1}{C_{1}}\right)}{8} + C_{1} + O\left(x^{6}\right)$$
Clasificación
factorable
1st power series
lie group