1. The problem statement, all variables and given/known data y'' + y = sin x + x*cos x 2. Relevant equations 3. The attempt at a solution i don't like undetermined coefficients. so far, for me, it's been so much trial and error, although i am getting a little faster at it. anyway, i didn't work out the homogeneous equation, but i can see it'll be something with complex roots. i worked out the part for sin x and got yp=-1/2*x*cos x. now, with x*cos x, i tried a*x2sin x + b*x2cos x. when i plug all this in to the original equation, i get (4ax + 2b) cos x + (2a+4bx)sin x. so, i think i need to get 4ax + 2b = x, and 2a+4bx=0, right? i don't see any other way than to let 4a =1, and 2b=0, but this doesn't work in getting 2a+4bx=0. am i making some dumb mistake?