Chapter 8.2, Problem 27E

What is the general form of the particular solution guar- anteed to exist by Theorem 6 of the linear nonhomogeneous recurrence relation $a_n=8a_{n-2}-16a_{n-4}+F\left(n\right)$ if

a) $F\left(n\right)=n^3$ ?

b) $F\left(n\right)={\left(-2\right)}^n$ ?

c) $F\left(n\right)=n{2}^n$ ?

d) $F\left(n\right)=n^2{4}^n$ ?

e) $F\left(n\right)=\left(n^2-2\right){\left(-2\right)}^n$ ?

f) $F\left(n\right)=n^4{2}^n$ ?

g) $F\left(n\right)=2$ ?