Find a particular solution for y"+y=sinx+xcosx

I used an initial guess of

yp(x)= Asinx+Bcosx+Cxcosx+Dxsinx

y'p(x)= Acosx-Bsinx-Cxsinx+Ccosx+Dxcosx+Dsinx

y"p(x)= -Asinx-Bcosx-Cxcosx-Csinx-Csinx-Dxsinx+Dcosx+Dcosx

I end up with the following system of equations to solve my coefficients

-A+A-C-C (sinx)=1(sinx)

-B+D+D+B(cosx)=0(cosx)

-C+C=1 (xcosx) How can this be??? 0=1??

-D+D=0 (xsinx)

Here's where I hit my snag. The answer has an x^2 power in it too. I'm stumped!