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Homework Help: Nonhomogeneous recurrence relations

  1. May 17, 2014 #1
    1. The problem statement, all variables and given/known data
    Solve the recurrence relation an = 3an−1 −2an−2 +3, a0 = a1 = 1.

    2. Relevant equations
    an = general solution + particular solution

    3. The attempt at a solution

    I started with finding the general solution, which was easy. it ended up being A12n + A0

    now I am having trouble solving the particular solution.

    since 3 is a constant, we use B as the particular solution this results in:

    B = 3B - 2B + 3

    which is where i am stuck. If anyone knows how to do this i would be very grateful :)
  2. jcsd
  3. May 17, 2014 #2


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    Science Advisor
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    Gold Member

    But a constant is part of the homogeneous solution, so it can't work for the NH. So, similar to what you would do in differential equations, try multiplying by ##n## instead of just a constant. So try ##a_n = Cn## and see if that can work for a particular solution.
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