# Nonhomogeneous recurrence relations

1. May 17, 2014

### Joe626

1. The problem statement, all variables and given/known data
Solve the recurrence relation an = 3an−1 −2an−2 +3, a0 = a1 = 1.

2. Relevant equations
an = general solution + particular solution

3. The attempt at a solution

I started with finding the general solution, which was easy. it ended up being A12n + A0

now I am having trouble solving the particular solution.

since 3 is a constant, we use B as the particular solution this results in:

B = 3B - 2B + 3

which is where i am stuck. If anyone knows how to do this i would be very grateful :)

2. May 17, 2014

### LCKurtz

But a constant is part of the homogeneous solution, so it can't work for the NH. So, similar to what you would do in differential equations, try multiplying by $n$ instead of just a constant. So try $a_n = Cn$ and see if that can work for a particular solution.