Homogeneous 1st order Differential Equation

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.

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

Which I work out to be

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! (Nod)