This is a question from a book in which I can't figure out, but it has no solutions at the back.(adsbygoogle = window.adsbygoogle || []).push({});

Find the general solution to the PDE:

xy u_{x}+ y^{2}(u_{y}) - 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!

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# Nonhomogeneous PDE with non-constant coefficients

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