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Homework Help: Finding a recursion relation

  1. May 7, 2010 #1
    1. The problem statement, all variables and given/known data

    I just have a problem with series solutions when I get to the point of needing to find the recursion relation........and a few other problems.

    2. Relevant equations

    Assume y can be written ∑anxn

    3. The attempt at a solution

    So, on y'' + xy' + 2y = 0, I got to the point of

    an+2=-an/(n+1). I wrote out a few n's but still can't figure out exactly what the relation is. A little help, maybe?

    On another problem, (1+x2)y'' - 4xy' + 6y = 0, I got the point of

    2a2 + 6a3x - 4a1x + 6a0 + 6a1x + [n=2 to ∞]∑( (n+1)(n+2)an+2 + (n-1)nan - 4nan + 6an)xn = 0.

    Now what? Detailed help would be much appreciated.
     
  2. jcsd
  3. May 7, 2010 #2

    tiny-tim

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    Hi Jamin2112! :smile:
    Hint: 7*5*3*1 = 7*6*5*4*3*2*1/(23*3*2*1) :wink:
    General method is to have onen=1(…)xn or ∑n=2(…)xn (whichever seems to work), from which you get a general recursion relation for an for n ≥ 1 (or n ≥ 2 or whichever), together with some stray terms that don't fit inside the ∑, and which give you the initial terms. :smile:
     
  4. May 7, 2010 #3
    So the stray terms are the initial conditions. They get set to zero, along with everything inside the sigma, right?
     
  5. May 7, 2010 #4

    tiny-tim

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