I need to find a real general solution to y'' + 9y = 18x + 36 sin3x
It's been awhile, but I think you can split it, so you find y'' +9y = 18x, and y'' +9y =36 sin(x), and then add the solution together. Oh, and also y'' + 9y = 0. The homogenous case is simple, for sin(x) and 18x, the guess method could work or maybe variation of parameters.