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Math Help - help with difference equations

  1. #1
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    help with difference equations

    Hello. So I am currently having problems with difference equations. The problem is:
    a[n] + 2a[n-1] = n .

    I am not sure where to begin. I'm not asking for an answer I just want to know what I need to do. I have tried looking up tutorials and such but they all seem very complicated. There is another problem I solved somewhat similar and I have attached my work.

    Any help would be appreciated.

    Thanks,

    Jimbo
    Attached Thumbnails Attached Thumbnails help with difference equations-work.jpg  
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  2. #2
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    In this case there is only one root r, the characteristic equation is given by
    the sum from k=0 to N of (a_k)(r^N-k)=0 where N=1 and a_k represents the coefficients e.g a_1=2
    Find r and then write down the solution as in your previous example.
    Hope this helps...
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  3. #3
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    Quote Originally Posted by jbm715 View Post
    Hello. So I am currently having problems with difference equations. The problem is:
    a[n] + 2a[n-1] = n .

    I am not sure where to begin. I'm not asking for an answer I just want to know what I need to do. I have tried looking up tutorials and such but they all seem very complicated. There is another problem I solved somewhat similar and I have attached my work.

    Any help would be appreciated.

    Thanks,

    Jimbo
    Try letting

    a_n = b_n + pn + q

    and choose p and q (constants) to transform your problem to

     <br />
b_n + 2 b_{n-1} =0.<br />
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