Hi guys, I've gotten so far with this but I'm stuck on what to do next:

Have I done the steps correctly? I followed what I was told but maybe I've made a mistake I cannot see.

$\displaystyle (2x^2+y^2)y'=2xy$

$\displaystyle y'= \frac{2(y/x)}{2+(y/x)^2}$

So by letting v=y/x and differentiating and substituting my value for v and dy/dx in I get the following seperable DE

$\displaystyle \int\frac{(-2+v^2)}{v^3} dv = \int(1/x) dx$

Which I work out to be

$\displaystyle \frac{1}{v^2} -\ln v = \ln x +C$

But Im unsure how to isolate v, I tried using maple and It gave me an answer using the Lambert W function which I've never seen before, so I'm sure I've made a mistake along the lines..

Any help is appreciated!