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Math Help - Series solution about a singular point--help with y(2)

  1. #1
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    Series solution about a singular point--help with y(2)

    The given equation is x(x-1)y'' + 3y' - 2y = 0.

    I was able to discern that a(k+1) = a(k) * [(k+r)(k+r-1)-2]/[(k+r+1)(k+r-3)], and the roots are 0 and 4. That recursive equation gives me the correct coefficients for a(0) through a(3), and of course, a(4) is undefined. But I can't get it right from a(5) on. I used the root 0 to get those first few a's; was I supposed to switch over to 4?
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  2. #2
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    Re: Series solution about a singular point--help with y(2)

    Regard the a_{4} coefficient from the r=0 case as being arbitrary and then calculate the remaining coefficients in terms of a_{4}.
    That gets you a solution containing two arbitrary constants, a_{0} and a_{4}, in which case you have the general solution of the differential equation.
    If you generate the series based on r=4, you will find that it duplicates the second part of the r=0 solution
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  3. #3
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    Re: Series solution about a singular point--help with y(2)

    Oh goodness--I made the remaining terms in terms of a(5), not a(4). Changing that fixed the problem.
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