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Math Help - Inhomogenous recurrence relation -> homogenous

  1. #1
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    Inhomogenous recurrence relation -> homogenous

    I have recurrence relation
    x_k- x_{k-1}= 7^k
    Any hints how I can take out the 7^k term?
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  2. #2
    MHF Contributor

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    Well, yes, just drop it! That is, the "associated homogeneous relation" is x_k- x_{k-1}= 0. Because the original recurrence relation is linear, its general solution is the sum of the general solution to the associated homogeneous relation and any one solution to the entire relation.
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  3. #3
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    I'm not sure I follow, could you show me how to go further with that?

    I take x_k - x_{k-1 }= 0
    Which gives me x^2-x = 0
    Which gives x = 0, x = 1

    Which would make for a general solution containing 0^k and 1^k..
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