I am trying to solve the following recurrence relation, but I am doing something wrong all the time when trying to find the particular solution, and I cannot figure out what.
$y_k+4y_{k-1}+4y_{k-2}=(-2)^k$
To try to find the particular solution, $y_k^p$, I do the following:
$y_k^p=Bk^2(-2)^k$, and I find that $B=1 \implies y_k^p=k^2(-2)^k $, which, even after I try to rewrite what WolframAlpha answers, is not even near (I know that the first part of WolframAlpha's answer is the homogeneous part).
What am I doing wrong here?