Solving differential equation $y^{(5)} + 2y^{(3)} + y' = 2x + \sin(x) + \cos(x)$

From the comment by GWu:
Your general solution involves $e^{ix}$ and $xe^{ix}$. So if you want the particular solution with $\sin x$ and $\cos x$ (which are disguised forms of $e^{ix}$ and $e^{-ix}$), then you have to try $A x^2\cos x + Bx^2\sin x$