# Homework Help: Solving a DE

1. Sep 18, 2011

### fluidistic

1. The problem statement, all variables and given/known data
I must calculate the general solution to the following (reducible to homogeneous) DE:
$(x^2y^2-1)y'+2xy^3=0$.
Hint: Use the substitution $y=z^\alpha$.

2. Relevant equations
The one given in the hint.

3. The attempt at a solution
So I've used the hint. This gave me $(x^2z^{2 \alpha }-1)\alpha z^{\alpha -1}+2xz^{3\alpha }=0$.
I factorized by $z^{\alpha -1}$ and I reach that $z^{\alpha -1}=0$ (thus z=0, thus y=0) or $z^{2\alpha } (\alpha x^2 +2xz)=\alpha$.
I ran out of ideas on the second condition. ( I don't think back-substituting $z^\alpha =y$ will help).
Any help is appreciated. Thanks!