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Homework Help: Help with Wronskian Equation

  1. Oct 9, 2014 #1
    1. The problem statement, all variables and given/known data
    W(t) = W(y1, y2) find the Wronskian.

    Equation for both y1 and y2: 81y'' + 90y' - 11y = 0

    y1(0) = 1
    y1'(0) = 0
    Calculated y1: (1/12)e^(-11/9 t) + (11/12)e^(1/9 t)

    y2(0) = 0
    y2'(0) = 1
    Calculated y2: (-3/4)e^(-11/9 t) + (3/4)e^(1/9 t)

    2. Relevant equations
    W(y1, y2) = |y1 y2 |
    | y1' y2' |
    3. The attempt at a solution
    After calculating y1 and y2, I don't seem to be able to do this determinant calculation. Mostly because it just doesn't look right, plugging in those giant equations and taking the derivative of them. Am I missing something here? Thanks for any help in advance.
    Last edited: Oct 9, 2014
  2. jcsd
  3. Oct 9, 2014 #2


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    Science Advisor
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    Gold Member

    Well, you didn't show us where these solutions came from so we can't check whether they are correct. But I suspect the idea isn't to calculate it directly like that. Does your text talk about Abel's theorem? There is a special equation that the Wronskian satisfies that relates ##W(0)## and the coefficients of your DE.
  4. Oct 9, 2014 #3
    Sorry, I have it now, and I have heard a little about Abel's Theorum, I'll try to find more information on it, thanks.

    Edit: I got it after abit of research on Abel's Theorum, thanks so much.
    Last edited: Oct 9, 2014
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