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Differential Equations: Non-homogeneous Series Expansion

  1. Dec 11, 2011 #1
    1. The problem statement, all variables and given/known data

    y'' + y' + y = 1 + x + x2

    2. Relevant equations

    y = Ʃ CN*xN N starts at 0
    y' = Ʃ N*CN*x(N-1) N starts at 1
    y'' = Ʃ N*(N-1)*CN*x(N-2) N starts at 2

    3. The attempt at a solution[/]
    I know how solve the equations using series when the equation would equal to 0. My main question about using series on a non-homogeneous differential equation is whether or not the varialbes on the right side have the Cx coefficients? Or would they be paired up with the x, x2, etc? I think I need some quick clarification on this.

    Thanks!
     
  2. jcsd
  3. Dec 11, 2011 #2

    LCKurtz

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    The Cn's only appear in your expressions for y and its derivatives. But you must take the powers of x on the other side into account for your recursion formulas. I assume you know that series isn't the easiest way for this problem.
     
  4. Dec 11, 2011 #3
    Thanks for clearing that up. The instructor covered only homogenous problems, and when I ran into one of these I was not entirely sure how to solve it with series.
     
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