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Math Help - non homogeneous linear recursion

  1. #1
    Junior Member
    Joined
    Sep 2010
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    26

    non homogeneous linear recursion

    I have a problem that says

    Find an explicit formula for an if a0=0 and an+1=an+2^n

    Can I convert this equation to

    an=-an+1-2^n?
    then keep solving as if it were a non-homogeneous equation?

    Sorry for my lack of use of latex.
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  2. #2
    Senior Member
    Joined
    Dec 2008
    Posts
    288
    No you need to find the solution to the homogeneous equation (take away 2^n) then try to find a particular solution (try c*2^n ) and then add these two together. Once you have do this all you need to do is solve for the initial conditions, it's just like solving a linear non-homogeneous 1st-order differential equation,
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