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Differential Equation - Series - Recurrence Relation

  1. Apr 23, 2015 #1
    1. (16+x2)-xy'+32y=0

    Seek a power series solution for the given differential equation about the given point x0 find the recurrence relation.
    So I used y=∑Anxn , found y' and y''
    then I substituted it into the original equation, distributed, made all x to the n power equal to xn, made the indexes 0, and added them all up.

    Then I solved for an+2 and got:

    (an-32an-ann(n-1))/(16(n+2)(n+1))=an+2


    The question asks for for the recurrence relation in the form of a2k+2 and a2k+3
    which are supposed to be the recurrence relation for even and odd terms.

    How do I put it into that format? I'm just not sure where to go from this point. Also can someone even verify if I did the first part of obtaining an+2 correctly?
     
  2. jcsd
  3. Apr 23, 2015 #2
    g9JGvhB.png

    Picture of attempted solution
     
  4. Apr 24, 2015 #3
    Never mind, I figured out the question. You can just substitute 2n+1 and 2n into all n's to get odd and even terms respectively.
     
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