y''+y=2*x*sin(x)

my Yp=(Ax+B)cos(x)+(Cx+D)sin(x)

but the answers say that Yp is supposed to be (Ax^2+Bx)cos(x)+(Cx^2+Dx)sin(x)

Can anyone explain why an extra x was multiplied in Yp?

When i put Yp in the equation (y''+y), it worked fine as in i didn't get 0=2*x*sin(x)

using superposition, already found Yc, so please don't thread derail.