Hello, I have this DE: y'' + 2y' - 3y = 8ex - 12e3x when I find homogeneous solution I get yh = c1ex + c2e-3x; so now to find the particular solution by method of undetermined coefficients, do I set y to smth like this: y = y1 + y2 where y1 = Axex, y2 = A3x ? since one of the solutions to auxiliary equation appears on the RHS of the DE and the other does not? I don't need the full solution, just confirmation/correction of this part. Thanks much! EDIT: if I take the fact that if y1 + y2 is a solution, then y1 is a solution and y2 is a solution. I guess I answered my own question.