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Math Help - Linear difference equations

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by louboutinlover View Post
    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.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by louboutinlover View Post
    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
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    Last edited by mr fantastic; April 2nd 2009 at 07:29 PM. Reason: No edit - just flagging the quesiton as having been moved from a duplicate posting of the question
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