My ODE textbook does not help me much here; and a large number of master's exam practice tests (with worked out solutions) also isn't helping me. I need someone to recommend a (preferably ONLINE) source that clearly states how to solves ODES using eigenfunction expansion. For example, y''+y=kcosx with y'(0)=0, y'(pie)=1. This is just an example of the type I want to learn how to solve. It seems that when the boundary conditions are homogeneous, this problem is easily solved by plugging in an infinite series: y=Sum(a_n*cos(nx)) into the left side, and then plugging in a different series: Sum(b_n*cosnx)=kcosx..then equating coefficients and getting the b_n's. BUT when the BC are non-homogeneous, there appears to be extra work. Help.