1. The problem statement, all variables and given/known data I started learning about solving non homogeneous linear differential equations in class and I am a bit clueless on how to solve them since I've never had a prior experience with much of differential equation. I am trying to find the particular solutions to the equation L''+w^2L=cn^2sin(nt)+w^2b where w,c,n are constants. 2. Relevant equations 3. The attempt at a solution First, I split the equation into two: Lp1=> L''+w^2L=w^2b Lp2=>L''+w^2L=cn^2sin(nt) Not quite sure how to solve for the particular solution for the first one. Lp2: We guess that L=Acos(nt)+Bsin(nt). Then we have L'=-nAsin(nt)+nBcos(nt) L''=-n^2Acos(nt)-n^2Bsin(nt)=-n^2(Acos(nt)+Bcos(nt)) Plugging back into the equation => (-n^2(Acos(nt)+Bcos(nt)))+w^2(Acos(nt)+Bsin(nt))=cn^2sin(nt) What do we do from here? Any help will be appreciated. EDIT: For the second particular solution, do we just solve for Acos(nt)+Bsin(nt) because we supposed that is L? In that case, I get Lp2=(cn^2sin(nt))/(w^2-n^2). Also, for the first solution, do we guess that Lp1 is a constant, so when we take the second derivative, L'' becomes 0, so it just becomes w^2L=w^2b, hence L=b?