Analytical solution for linear second order PDE with two space variables

Question

I appreciate if anyone can help me with the solution of below PDE $u(x,y)$ $$u_{xx}(ax+b)+u_x(cx+d)+u_y(ey)+u(f\frac{y^2}{x}+gx)=h(x,y)$$ where a,b,c,d,e,f,g are constants and h is a function of exponential of x and y. I reached to this problem as a midpoint for the solution of a bigger problem. My first guess was the separation of variables but $u(f\frac{y^2}{x}+gx)$ was my problem. Now, I am thinking about using the method of characteristics. Please let me know if you need further information. I really appreciate your help.