How Do I Solve This Interesting But Challenging ODE?

[gvk]

Very simple in writing, but hard to solve:
x*\frac{dy}{dx}=(y^2-y x^2)/(y^2+x^2)

 

[amcavoy]

Very simple in writing, but hard to solve:
x*\frac{dy}{dx}=(y^2-y x^2)/(y^2+x^2)

Maybe convert to polar coodinates? That x²+y² wants to be r². Maybe not though

Alex

 

[saltydog]

Very simple in writing, but hard to solve:
x*\frac{dy}{dx}=(y^2-y x^2)/(y^2+x^2)

I tend to look at it this way:

(y^2-yx^2)dx-(xy^2+x^3)dy=0

but are unable to proceed. It's not exact, can't make it exact, and can't come up with any differentials by inspection.