I am trying to help a friend of mine solve
$$ a_n + 5 a_{n-1} + 6 a_{n-2} = 12n - 2(-1)^n$$
Now the homogenous solution is easy to find, and one just needs to solve the equation $r^2 + 5r + 6 = 0$ Which has roots $r=-2$ and $r-3$, so the homogenous solution is
$$A (-2)^n + B (-3)^n$$
Which can be confirmed by putting it into the equation. Now usually I would guess that the particular solution was on the form
$$h_p = (An + B) + C(-1)^n$$
but this is clearly wrong, is there any other way to find the solution of the equation ?