Solving Non-Homogeneous Differential Equations with Two y' Terms

[Questions999]

Homework Statement

I have to find the differential of (y-xy')^2=x^2+y^2.Now,I have solved hom. equations but this is different because there are two y'. I know how to prove that it is a hom. equation of degree zero, so we can skip that, but how to solve this? Some hints would be highly appreciated.

Homework Equations

The Attempt at a Solution

 

[the_wolfman]

What happens if you take the square root of both sides of the equation?

 

[Questions999]

(y-xy')=sqrt(x^2+y^2)

 

[the_wolfman]

Do you know how to solve homogeneous equations of the form y'= f(x,y)?

Can you write (y-xy')=sqrt(x^2+y^2) as y'=f(x,y)?