Wave equation with linear coefficients

The following pde came up in a physics problem: $$(Cy+D)\frac{\partial^2 u}{\partial x^2}-(Ay+B)\frac{\partial u^2}{\partial y^2}-A\frac{\partial u}{\partial y} =f(x,y),$$ A,B,C,D are fixed constants.

I'm not very experienced at solving pde-s, so before I immerse myself into the subject I would like to ask some experts if they know a simple way to solve it, or know about its solution in the literature.