# Linear difference equations

• Mar 30th 2009, 09:01 AM
louboutinlover
Linear difference equations
there are two questions in the attachment with the correct answers.

i have worked through the questions, to my knowledge, however seem to be only a few steps short of reaching the actual solution on each of the questions.

• Mar 30th 2009, 01:37 PM
Jester
Quote:

Originally Posted by louboutinlover
there are two questions in the attachment with the correct answers.

i have worked through the questions, to my knowledge, however seem to be only a few steps short of reaching the actual solution on each of the questions.

1) You have $\displaystyle y_t = A \left(\frac{1}{2}\right)^t + B 2^t + 1$. Requiring that yt stays finite as $\displaystyle t \to \infty$ gives B = 0. Then use your IC.

2) Seek a particluar solution $\displaystyle y_{pr} = k r$, the l isn't need, it's in the complimentary solution. Subs into the difference equation

$\displaystyle k(r+2) - 4k(r+1) + 3kr = 4$ and expand. This gives $\displaystyle k = -2$ and hence your solution.
• Mar 31st 2009, 02:52 AM
CaptainBlack
Quote:

Originally Posted by louboutinlover
there are two questions in the attachment with the correct answers.

i have worked through the questions, to my knowledge, however seem to be only a few steps short of reaching the actual solution on each of the questions.

The condition that $\displaystyle y_t$ is always finite means that $\displaystyle B$ must be zero, and that $\displaystyle y_0=2$ then means that $\displaystyle A=1$.
For 1b you have an $\displaystyle r$ on the right hand side that should not be there.