I'm stuck on just one problem. 1. The problem statement, all variables and given/known data 2y'' + 3y' + y = t2 + 3sin(t) 2. Relevant equations It says in the lesson that if you have a polynomial, guess a solution is "Yi(t)= Ts(A0tn + A1tn-1 + .......... + An) where s is the smallest nonnegative integer (s=0,1, or 2) that will ensure that no terms in Yi(t) is a solution of the corresponding homogeneous equation." And I don't really understand that jargon. Maybe someone could dumb it down for me. 3. The attempt at a solution Since the solution is the sum of two different functions, t2 and 3sin(t), I can solve the differential equation for each individually, and them add them together at the end since the sum of the solutions to a differential equation is also a solution. I got the solution to 2y'' + 3y' + y = 3sin(t). It is Y1(t) = (-3/10)sin(t) -(9/10)cos(t) But Y2(t) is giving me trouble. I guessed Y2(t) = A0t2 + A1t + A2 but ended up with a system equations that still had t in it; thus I couldn't solve it. Set me on the right track.