Solving x²-2px+y²-2(y-p)y'y=0

[Kvad]

Hi all,

I have derived a differential equation, which I don't know how to solve. I can do some numerical simulations, but would really be interested in, at least, knowing if an analytical solution exists, so would appreciate any help with it: (I have removed argument from y)

x²-2px+y²-2(y-p)y'y=0

Usually I just solve equations with mathematica, but it cannot tackle this one, though it doesn't look too bad...

Thanks!

 

[mfb]

The part without explitic x-dependence leads to the product log function (WolframAlpha), I don't see an obvious way to take the other part into account.