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Using the Frobenius Method - 2nd order DE

  1. Sep 11, 2011 #1
    Using the Frobenius Method -- 2nd order DE

    1. The problem statement, all variables and given/known data

    y"+(1/sinx)y'+((1-x)/x^2)y=0

    Find the indicial equation and forms of two linearly independent expansions about x=0. Don't find the coefficents.



    2. Relevant equations



    3. The attempt at a solution The singular points at n*pi are regular, and thus I need to use the method of Frobenius. I normally don't have a problem using this method, but I am a bit thrown off by the (1/sinx) term. I tried rewriting the DE as (x^2)*sin(x)*y"+(x^2)*y'+sin(x)*(1-x)y=0, thinking that it might be a good idea to write sin(x) as an expansion. But then I end up with a double summation, and I'm not sure how to get the indicial equation out of it first of all. And I am not sure what it means by "find the forms of the two linearly independent expansions..." Anyway, I attached a PDF showing my work and where I got stuck. Any hints would be greatly appreciated.
     

    Attached Files:

  2. jcsd
  3. Sep 17, 2011 #2
    Re: Using the Frobenius Method -- 2nd order DE

    Never mind.
     
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