This is my question.

Find the complete integral of the PDE

$\displaystyle \frac {\partial ^2 u}{\partial x^2} +2 \frac {\partial ^2 u}{\partial x \partial y}+ \frac{\partial ^2 u}{\partial y^2} $ = x e^{x+y}

involving arbitrary functions f1 and f2

A little nudge towards the right direction would be of great help. I'm sure I can take it from there...