$$y''(x)+4y'(x)+3y(x)=9x^2-20+30e^{2x}, \quad y(0)=0, \quad y'(0)=2$$
I'm stuck on finding a particular integral for the non-homogeneous R.H.S.: $9x^2 − 20 + 30e^{2x}$.
So $y= y_c + y_p$. I found $y_c = C_1e^{-x} + C_2e^{-3x}$ (where $C_1$ and $C_2$ are constants) But what would I try for $y_p$? If it helps, I know how to do it if it's just a polynomial (i.e. for a 2nd degree polynomial): you set $y_p= Ax^2 + Bx + C$ and $y'_p= Ax + B$ and $y''_p= A$
But in this case we have different things. What would I need to do? I would really appreciate your help. Thanks in advance!