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Theoretical/non-tedious question about Frobenius method

  1. Apr 18, 2012 #1

    s3a

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    When using the Frobenius method of solving differential equations using power series solutions, I get a solution

    y = (indicial_stuff) + (infinite_summation_stuff) = 0

    for a differential equation differential_stuff = 0.

    WHY is it that I can say

    (indicial_stuff) = 0?

    If

    y = (indicial_stuff) * (infinite_summation_stuff) = 0

    (NOTICE THE MULTIPLICATION INSTEAD OF ADDITION) then it would make sense to me that

    (indicial_stuff) = 0

    but with the addition, I cannot make sense of this.

    I tried to generalize this question and hope that I haven't made it more confusing but, if I have made the question confusing, please tell me and I will clear things up as best as I can.

    Basically, I'm just asking for the reason why this – the isolation of the indicial polynomial equation (and the other summation portion) - is justified.

    Any input would be greatly appreciated!
    Thanks in advance!
     
  2. jcsd
  3. Apr 19, 2012 #2

    s3a

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    The answer to my question was: "by equating coefficients."
     
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