Help with 1st order ODE of degree 4

Hello everyone,

I have this ODE and I am afraid I've got the wrong approach...

Here's the DE:

$\displaystyle y'=\frac{y^{4}+x^{2}\,y^{2}-9\,x^{4}} {x\,y^{3}}$

I'm thinking that we may replace $\displaystyle y'$ by $\displaystyle dy/dx$ so that the DE becomes separable. Then we set $\displaystyle x=vy$ so that we get rid of x and the only 2 variable remaining would be v and y...

but I got to the point where $\displaystyle -dy/dy=\frac{dv}{v^{3}\,(9v-1)}$

Have I got the right approach...

Thanks for any help...