- #1

chatterbug219

- 15

- 0

## Homework Statement

Solve the difference equation: a

_{n+2}- 5a

_{n+1}+ 6a

_{n}= 4

^{n}

Subject to a

_{0}= 0 & a

_{1}= 1

## Homework Equations

a

_{n}= Ar

^{n}

## The Attempt at a Solution

I got two solutions for the first part for when it is homogeneous by substituting a

_{n}= Ar

^{n}into the equation and solving for r.

a

_{n}= A(3)

^{n}

a

_{n}= A(2)

^{n}

I just don't know where to start for non-homogeneous. I tried a

_{n}= B*4

^{n}and I got B*4

^{n+2}-5B*4

^{n+1}+ 6B*4

^{n}= 4

^{n}but I don't know where to go from there.