I understand why this is a good method, but in one of the problems I am trying I yield 4 unknown parameters in a second order differential equation. I believe I should only have 2. Let f(x) be a part of a homogeneous solution and and u(x) be some unknown function in x. Then a particular solution to the inhomogeneous eqn is y = f(x)u(x). Subbing this in to the differential eqn and cancelling, you get a differential eqn in u(x). Now then solving this will give more integration constants. I think this may be my problem. Is there a reason why we don't include integration constants at this stage?