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Math Help - Wronskian

  1. #1
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    Wronskian

    I am stuck on this question, I would appreciate any help.

    If y1 and y2 are linearly independent solutions of


     ty^{''} +2y^{'} +te^{4t}y =0

    And if W(y1,y2)(1) = 2, find W(y1,y2)(3)

    Thanks for any help.
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  2. #2
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    Quote Originally Posted by Oblivionwarrior View Post
     ty^{''} +2y^{'} +te^{4t}y =0

    And if W(y1,y2)(1) = 2, find W(y1,y2)(3)
    I assume t>0 and in that case write:
    y'' + \frac{2}{t}y' + e^{4t}y=0

    Then W(y_1,y_2) = a \cdot e^{-\int \frac{2}{t} dt} = a\cdot e^{ - 2\ln t} = \frac{a}{t^2}.

    Since W(y_1,y_2)(1) = 2 \implies \frac{a}{1^2} = 2 \implies a=2.

    Now you can find W(y_1,y_2)(3)
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  3. #3
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    Abel's Theorem, of course!
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