1. The problem statement, all variables and given/known data consider y'' + 2y' - 3y = 1 + xe^x, find the particular solution 3. The attempt at a solution so f(x) = 1 + xe^x f'(x) =e^x + xe^x f''(x) = 2e^x + xe^x so it looks like my particular solution is going to have a constant term, an e^x term and an xe^x term, so I can write Particular Solution: y(x) = A + Be^x + Cxe^x and then differentiate this twice and plug into the original equation? Is this on the correct track? I ask because an online source says that I should have y(x) = A + Bxe^x + C(x^2)e^x can someone help me understand why I am wrong if I am wrong? Why have an (x^2)e^x but no e^x?