Obtain a general solution of

x^2(dU/dx) + y^2(dU/dy) = (x+y)U

Hint: Note that the characteristics imply

dy/y^2 = (dx-dy)/(x^2-y^2)

My attempt:

(x^2 - y^2)dy = y^2(dx-dy)

x^2dy - y^2dy = y^2dx - y^2dy

x^2dy = y^2dx.

Integrating both sides gives

x^2y = y^2x + c

where I get stuck