1. The problem statement, all variables and given/known data y''+y=3sin2t+2tcos2t 2. Relevant equations 3. The attempt at a solution I tried doing this problem by breaking it into 3 others. It doesn't quite work, and I want to know why. First, I solved for the nonhomog part of: y''+y=3sin2t Which is Y1 = -sin2t Then, I did the same with y''+y = 2t which is Y2 = 2t Lastly, I did y''+y=cos2t Which is Y3 = -(1/3)cos2t Combining these with the homog. parts gives me: y = c1cost + c2sint - (2/3)tcos2t -sin2t But, this is not quite right, as the -sin2t should be -(1/9)sin2t. What is incorrect about breaking the DE up and putting it back together in this way? Thank you!