Sr Examen
Ecuación diferencial ydx=(y-xy^2)dy
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Solución
Ha introducido
[src]
d 2 d
y(x) = --(y(x))*y(x) - x*y (x)*--(y(x))
dx dx
$$y{\left(x \right)} = - x y^{2}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + y{\left(x \right)} \frac{d}{d x} y{\left(x \right)}$$
y = -x*y^2*y' + y*y'
Respuesta
[src]
y(x) = 0
$$y{\left(x \right)} = 0$$
2 / ___ \
y (x) ___ ____ |\/ 2 *y(x)|
----- \/ 2 *\/ pi *erfi|----------|
2 \ 2 /
x*e - ----------------------------- = C1
2
$$x e^{\frac{y^{2}{\left(x \right)}}{2}} - \frac{\sqrt{2} \sqrt{\pi} \operatorname{erfi}{\left(\frac{\sqrt{2} y{\left(x \right)}}{2} \right)}}{2} = C_{1}$$
Clasificación
factorable
1st exact
1st power series
lie group
1st exact Integral