Integrating a differential equation

[macaroni]

Homework Statement

y' = 2xy/(x^2-y^2)

answer: Cy = x^2 + y^2

Homework Equations

The Attempt at a Solution

dy/dx = 2xy/(x^2-y^2)
dy = [2xy/(x^2-y^2)]dx

how do i separate the variables?

 

[Billy Bob]

In the form 2xy dx + (y^2-x^2) dy, the coefficients are both homogeneous and of degree two, so the substitution y=vx will work. Kind of long way to do it, but it works.