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Recurrence Relation

  1. Nov 14, 2007 #1
    [SOLVED] Recurrence Relation

    1. The problem statement, all variables and given/known data

    Solve the recurrence relation

    2. Relevant equations

    add the homogeneous solution to the particular solution

    3. The attempt at a solution

    Characteristic: [itex]s^2+3s+2=0 \Rightarrow x=-2,-1[/itex]

    Homogeneous: [itex]a_n=A(-2)^n+Bn(-1)^n[/itex]

    (*here is where I'm not sure if I've gone wrong. Should it be
    [itex]a_n=A(-1)^n+Bn(-2)^n[/itex] instead? How would I know?*)
    anyway, not sure I've right up to here but onwards->

    Particular: [itex]a_n=C3^n[/itex]

    then [tex]C3^{n+2}+3C3^{n+1}+2C3^n=3^n[/tex]

    letting n=0 yeilds[tex]a_n=\frac{3^n}{20}[/tex] for the particular solution

    then the solution is [tex]a_n=A(-2)^n+Bn(-1)^n+\frac{3^n}{20}[/tex]

    solving for A and B I got A=-1/20 and B=-3/4 and putting it all together seemed to give me nonsense.

    Anyway, as you can probably see I'm not really understanding what's happening here. I would really appreciate nudge in the right direction.

    Thank you kindly for you time
  2. jcsd
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