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Solving DE using power series

  1. Oct 22, 2009 #1
    1. The problem statement, all variables and given/known data

    Solve this equation using power series: y'' + y = x



    2. Relevant equations

    none

    3. The attempt at a solution

    I am confused about the x on the RHS of the equation. If the equation was y'' + y = 0, I would have no problem solving it. I am just a little confused about how the x fits into the equation for cn.

    if the equation were y'' + y = 0, then cn + 2 = cn/(n+1)(n+2). How does the x fit into this?
     
  2. jcsd
  3. Oct 22, 2009 #2

    Mark44

    Staff: Mentor

    You should be able to split up the series you get into three parts. One of those parts will be very short, with just a single term.

    Show us what you have for your series.
     
  4. Oct 22, 2009 #3
    I'm a newb and don't know how to use this website, so here goes:

    SUM[ (n+2)(n+1)cn+2xn] + SUM[cnxn] = x
     
  5. Oct 22, 2009 #4
    [tex]
    \ \ \sum_{n=0}^{\infty}{(n+2)(n+1)c_{n+2}x^n} \ \ + \ \ \sum_{n=0}^{\infty}{c_{n}x^n} \ \ = x
    [/tex]

    Here it is in the non-retarded version
     
    Last edited: Oct 22, 2009
  6. Oct 22, 2009 #5

    Mark44

    Staff: Mentor

    Try expanding your two series and then grouping the results by powers of x. Be sure to take the x on the right side into account.
     
  7. Oct 24, 2009 #6
    I kind of understand what you're saying, but could you try being a little more specific? I am terrible with series.
     
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