I'm modeling the dynamic localization, after solving the Helmholtz equation I obtained this partial differential equation, if anybody can give me a guideline I would be truly grateful.
$$ i\alpha(y) \frac{\partial^2 u(x,y)}{\partial x^2} + \beta (y)\frac{\partial u(x,y)}{\partial x} + \frac{\partial u(x,y)}{\partial y} - iA\cos (x) u(x,y) = 0.$$