Problems: Section 5.4

For each difference equation in [1 10], state its order and whether it is linear. If it is linear, state if it is homogeneous; if it has constant coefficients.

1.	a _n=2 /a _n _?1.
2.	w _n =max{ w _n _?1, w _n _?3}.
3.	h _n ₊₁=2 h _n+1.
4.	a _n _?2=2 ⁿ a _n _?6 +( ?3) ⁿ.
5.	F _n= F _n _?1+ F _n _?2.
6.	P _k ₊₁= P _k (1+ r) ? P _k rt.
7.	d _n =(n ?1) (d _n _?1+ d _n _?2).
8.	.
9.	.
10.	.
11.	The text defined classifications only for difference equations for a single sequence involving a single index variable. Nonetheless, we think you can figure out reasonable classifications for the following. Do so. C(u, b)=C( u ?1, b)+ C( u, b* ?1)
12.	Show that every second-order, nonhomogeneous, constant-coefficient difference equation with geometric nonhomogeneous part meets the assumptions of Theorem 1. (That is, you have to show that f is defined wherever it is supposed to be.) A geometric nonhomogeneous part is an expression of the form ar ⁿ for some nonzero constants a and r.
13.	Consider the difference equation Suppose that we set initial conditions r ₀=1, r ₁=2. Show that...