1. The problem statement, all variables and given/known data Find the general solution. 2. Relevant equations y"+y=x2sin2x 3. The attempt at a solution Characteristic equation would be: m2 + 1 = 0 So,m2 = -1 Therefore, m = i or m = -i. Complementary function would be : Asinx+Bcosx where,A and B are constants respectively. If I write the particular integral as (Cx2+Dx+E)sin2x + (Px2+Qx+R)cos2x Then,it would be very tedious to solve. Is there any alternative way like writing sin2x as Imaginary part of ei2x and then solving the particular integral?