I'm having some trouble with this reccurence problem. Usually we have just one term like $2^n$ or $3n$, but this time there one of each kind. $$\begin{align} a_{n}=5a_{n-1} - 6a_{n-2} + 2^n + 3n \end{align}$$
A hint is to use when looking for the particular solution is to use the form: $$\begin{align} qn2^n + p_1n + p_2 \end{align}$$
I started with the homogenous solution, which is the easy part. I got $$\begin{align} a_{n}^{(h)}=5a_{n-1} - 6a_{n-2} \implies&& r_1 = 2,&& r_2 = 3\\ a_n^{(h)} = \alpha_1 3^n + \alpha_2 2^n \end{align}$$ Then I tried with the particular solution (By using the hints form), but I got nowhere. Any reflections/pointers?