# Linear difference equations

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• Mar 30th 2009, 10:01 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.

please help
• Mar 30th 2009, 02:37 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.

please help

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

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

$k(r+2) - 4k(r+1) + 3kr = 4$ and expand. This gives $k = -2$ and hence your solution.
• Mar 31st 2009, 03:52 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.

please help

For question 1a you have the complementary function and a particular solution. The general solution is the sum of these.

The condition that $y_t$ is always finite means that $B$ must be zero, and that $y_0=2$ then means that $A=1$.

For 1b you have an $r$ on the right hand side that should not be there.

CB