I am looking for the form of a solution for a second order ODE with right hand side: x (sin x + 2) I'm thinking the form would be (Ax + B) sin(x) + (Cx + D) cos(x) + Ex + F. Does this seem correct? Thanks for any help or suggestions!
Have you tried it? That would tell you whether it is correct or not! If it is correct, you will get an answer. If it is not correct, you won't. Actually, it is impossible for us to tell because you haven't given us the homogeneous equation or its solutions. If sin(x) or cos(x) or x sin(x) or x cos(x) are already solutions to the homogenous equation, you will need to multiply (Ax+B)sin(x) and (Cx+ D)cos(x) by x again. If x or a constant is already a solution to the homogeneous equation, you will need to Ex^{2}+ Fx.