From my own experience, it would be worth trying to use the Ritz/Galerkin method. This makes finding a solution to the equation a minimal task, which Maple seems to be good at. There is a lot of literature on the Ritz/Galerkin method. I will just say this: A plausible approach to a solution function with free parameters to be calculated is chosen, e.g. as a linear combination. The so-called equation defect must then be minimized. This is basically a positive definite measure for the difference "left side minus right side" of the equation.