1. The problem statement, all variables and given/known data Particular solution of y" - y' - 2y = e^(2x) 2. Relevant equations None 3. The attempt at a solution This makes no sense to me, why do I have to use the solution of the form y(t) = cxe^(2x) For the problem above, but when I switch the signs and it becomes y" - y' + 2y = e^(2x) (notice the +2 in front of y) The solution becomes y(t) = ce^(2x) I get that it WORKS, but why? Am I seriously supposed to remember hundreds of forms for solutions when I solve these types of DE's or do I solve these with trial and error? It's ridiculously tedious trying several different forms just to realize it doesnt work at the end.