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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
Try looking here
http://www.mathhelpforum.com/math-he...u_y-x-y-u.html