How do we solve recurrence equations of the form:
$ax_{n+1}+bx_n+cx_{n-1}=dn^p+e\;,$ where $a,b,c,d,e$ are constants and $p\in \mathbb Z$?
Perhaps we could first solve the homogeneous equation $ax_{n+1}+bx_n+cx_{n-1}=0\;.$ Then we find the particular solution... but how? Guesswork?
Thanks.