Sr Examen
Ecuación diferencial dx*(x*y^3+x)+dy*(x^2*y^3-y^3)=0
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Solución
Ha introducido
[src]
3 3 d 2 3 d
x + x*y (x) - y (x)*--(y(x)) + x *y (x)*--(y(x)) = 0
dx dx
$$x^{2} y^{3}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + x y^{3}{\left(x \right)} + x - y^{3}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
x^2*y^3*y' + x*y^3 + x - y^3*y' = 0
Respuesta
[src]
/ ___ \
___ |\/ 3 *(-1 + 2*y(x))|
/ 2\ / 2 \ \/ 3 *atan|-------------------|
log\-1 + x / log(1 + y(x)) log\1 + y (x) - y(x)/ \ 3 /
------------ - ------------- + --------------------- - ------------------------------- + y(x) = C1
2 3 6 3
$$y{\left(x \right)} + \frac{\log{\left(x^{2} - 1 \right)}}{2} - \frac{\log{\left(y{\left(x \right)} + 1 \right)}}{3} + \frac{\log{\left(y^{2}{\left(x \right)} - y{\left(x \right)} + 1 \right)}}{6} - \frac{\sqrt{3} \operatorname{atan}{\left(\frac{\sqrt{3} \left(2 y{\left(x \right)} - 1\right)}{3} \right)}}{3} = C_{1}$$
Clasificación
separable
1st exact
1st power series
lie group
separable Integral
1st exact Integral