Find the solution:

$\displaystyle xy dx - (x^{2}+y^{2}) dy =0 $

So far I have:

$\displaystyle y=vx$

$\displaystyle dy=vdx+xdv$

Plug the $\displaystyle y $ and $\displaystyle dy $ into the equation to get:

$\displaystyle x(vx) dx -(x^{2}+(vx)^{2}) (vdx+xdv)=0$

$\displaystyle vx^{2} dx -[vx^{2} dx+ x^{3} dv+ v^{3}x^{2}dx+v^{2}x^{3}dv]=0 $

No matter what I do, I'm just going in circles. I can't seem to get the variables separated.