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Math Help - Nonhomogenous dynamical systems

  1. #1
    Junior Member
    Joined
    Sep 2009
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    Question Nonhomogenous dynamical systems

    Find the general solution to the following:

     A(n+1)=2A(n)+3^n-n

    and find the particular solution when A(0)=1.

    I have like ten problems this way.

    After all my calulations i got A(k)=c2^k-3^k+k
    is this right? I'm lost on how to find the particular solution. Can anyone help?
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  2. #2
    Member mohammadfawaz's Avatar
    Joined
    Feb 2010
    From
    Lebanon - Beirut
    Posts
    100
    Well, to check your answer, simply try to plug in the result you got in the given difference equation. I think your solution is not 100% correct. The general form of the solution should be a2^k+b3^k+ck. Plug in the given equation and compare to find a,b and c. To find the particular solution, you have to put k = 0 in the general solution. We have to get 1. So, you find the missing parameter. For example, assuming your answer is correct, and we know A(0)=1, then: c2^0-3^0-0=1. Therefore, c=2.
    hope this helps
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