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Solve first order difference equation!

  1. Dec 5, 2011 #1
    1. The problem statement, all variables and given/known data
    Solve the first order difference equation.

    2. Relevant equations
    x[n] - x[n-1] = n(n+1)/2
    x[1] = 1

    3. The attempt at a solution
    Homogenous solution:
    Characteristic equation:
    r - 1 = 0 <=> r = 1
    => yhn = C * 1^n = C

    Particular solution:
    ypn = ?
    I'm supposed to do some intelligent guess here. n(n+1)/2 is a polynomial of degree 2 and dosnt exist in yhn so i should be something like An(n+1) or An^2+Bn but Ican't get anything to work.
  2. jcsd
  3. Dec 5, 2011 #2


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    Science Advisor
    Homework Helper

    I would guess a polynomial of order 1 degree higher than n(n+1)/2. Say An^3+Bn^2+Cn.
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