Im having some troubles with solving the following nonhomogeneous recurrence, i will only post the non-homogenous part of the recurrence as that is the part i dont understand: $4^n * \cos(\pi*n)$,
The homogenous part of the recurrence is $A*(-4)^n$
Now i did some solving myself and got to the following form for the particual part of the recurrence and was wondering if it is correct or not.
$ 4^n*( B*\sin(\pi n) + C*\cos(\pi n))$
Edit Adding Whole equation
$a_{n+1} + 4a_n = 4^n * cos(\pi n)$
If you aren't afraid of complex numbers, you see that you can write your recurrence as:
$\begin{align*} a_{n + 1} + 4 a_n &= \frac{\exp(n \pi i) + \exp(-n \pi i)}{2} \end{align*}$
The forcing function is now a sum of powers, and the solution routine. Translate back into trigonometric functions at the end.