Does anyone know a method to solve this PDE?

$\displaystyle \frac{\partial^2y}{\partial x^2}+f_1(x,t)\frac{\partial y}{\partial x}=f_2(x,t)\frac{\partial y}{\partial t}+f_3(x,t)$

$\displaystyle f_1$, $\displaystyle f_2$ and $\displaystyle f_3$ are three functions of x and t. I wanted to try Laplace transform but it becomes very complicated due to presence of $\displaystyle f$ functions. If initial and boundary conditions are required I can provide them.

Thank you,