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Find a recurrence formula for the power series solution around t = 0

  1. Feb 26, 2012 #1

    s3a

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    1. The problem statement, all variables and given/known data
    Find a recurrence formula for the power series solution around t = 0 for the differential equation:

    d^2 y/dt^2 + (t - 1) dy/dt + (2t - 3)y = 0


    2. Relevant equations
    y = Σn=0 to inf (a_n * t^n)
    and formula to differentiate polynomials.


    3. The attempt at a solution
    I can't find a way to bring all the sums to the same index. I've though about the fact that I can just change which index the sum is at for some of the sums because n=0 and n=1 could cause the entire term to be 0 itself but everything I think about seems to have at least one of the sums starting from another index. My attempt at a solution is attached.
     

    Attached Files:

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