This is a question from a book in which I can't figure out, but it has no solutions at the back. Find the general solution to the PDE: xy ux + y2 (uy) - y u = y - x I've learnt methods such as change of variables and characteristic curves, but I'm not sure how I can apply them in this situation. The PDE is nonhomogeneous, with non-constant coefficients, and there is an "u" term. Can somebody help? Thank you!