# Thread: Xn Solving a difference equation

1. ## Xn Solving a difference equation

Find Xn

X(n+2) - 5X(n+1) +6Xn = 2*3^n

2. Originally Posted by Knut-o
Find Xn

X(n+2) - 5X(n+1) +6Xn = 2*3^n

This is a difference equation with constant coefficients. Your class notes should tell you what to do.

Find the solution to $\displaystyle X_{n+2} - 5 X_{n+1} + 6 X_n = 0$.

Construct a particular solution.

Now add those two solutions together.

If you need more help please show what you've done and say where you get stuck.

3. I´m stuck at the particular solution. Am I suppose to use "A * E*3^n" at the left side to find it?

4. Originally Posted by Knut-o
I´m stuck at the particular solution. Am I suppose to use "A * E*3^n" at the left side to find it?
Since $\displaystyle 3^n$ is part of the homogenous solution you can't try to construct a particular solution of the form $\displaystyle X_n = \alpha 3^n$. Instead you have to try a particular solution of the form $\displaystyle X_n = \alpha {\color{red}n} 3^n$.

5. ok, thank you