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Homework Help: Nonhomogeneous difference equation question

  1. May 9, 2012 #1
    1. The problem statement, all variables and given/known data
    Find the general solution

    2. Relevant equations

    3. The attempt at a solution
    I start out by solving the homogeneous equation and end up with the two roots 1 and 2.

    Then I try to use the method of undetermined coefficients to find a particular solution.

    I guess that the solution is of the following form (I should probably include a cos term as well)






    I then insert these equations into the original equation to get


    move the terms around a bit to get


    From the first part I see that




    I would like to do something similar for the sin part of the expression, but I'm not sure how to handle it.
    I tried with sin(0.5π(t+2))=sin(0.5πt+π)=-sin(0.5πt) but then I don't know what to do with sin(0.5(t+1)).

    If anyone has any hints, tips or tricks I would be happy.

    I hope the equations are understandable otherwise I'll post them as a picture.

    Thanks in advance.
  2. jcsd
  3. May 9, 2012 #2


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    Gold Member

    Is this your original equation? It doesn't look like a non-homogeneous ODE to me.
    I just noticed in your title you call it a "difference equation" and not "differential equation", in which case, i might have misunderstood the problem.
  4. May 9, 2012 #3
    I just realized I can do subscripts. The original problem is this:


    Yeah it's a difference equation so we only have discrete moments of time.
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