I have to solve this ODE:
$$(D^2+3D+2)y=4\cos^2x$$
where $D^n$ refers to the differential operator $\frac{d^n}{dx^n}$. I have gotten the complementary function as,
$$CF=c_1e^{-2x}+c_2e^{-x}$$
But I couldn't find the particular equation. As far as I know, we must guess a generic solution, such that it's second and first derivatives have the "$\cos^2x$" term in them. However, I can't seem to find any that can satisfy this. Please guide me in solving this equation.
Hints: Reduce non-homogeneous part $4\cos^2x$ to $2(1+\cos2x)$ then try separately.