I'm trying to solve the equation:
$ \frac{\partial U}{\partial x} + 2 \frac{\partial U}{\partial y} + (2x-y) U = 2x^2 + 3xy - 2y^2 $
I'm assuming this requires a change of variables but I'm not so sure about how to pick appropriately. An explanation of the procedure would be appreciated.
The answer is $ U = x + 2y + \frac{5}{y-2x} + e^{\frac{1}{5}(-2x^2 - 3xy + 2y^2)} f(y-2x) $