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Math Help - Hard differential equation

  1. #1
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    Hard differential equation

    y''+6y'+9y = e^(-3x)/X^3

    I don't know what to do when b^2-4ac is zero. When I do the Wronskien matrix I can't solve for C1 and C2 cause my y1 and y2 are the same:

    x^2 + 6x + 9 = 0

    delta = 0

    Y(x) = c1e^-3x + c2e^-3x

    Can anyone help?
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Provoke View Post
    y''+6y'+9y = e^(-3x)/X^3

    I don't know what to do when b^2-4ac is zero. When I do the Wronskien matrix I can't solve for C1 and C2 cause my y1 and y2 are the same:

    x^2 + 6x + 9 = 0

    delta = 0

    Y(x) = c1e^-3x + c2e^-3x

    Can anyone help?
    y(x)=c_1e^{-3x}+c_2{\color{red}x}e^{-3x}, since you have repeated roots.
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  3. #3
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    Quote Originally Posted by Chris L T521 View Post
    y(x)=c_1e^{-3x}+c_2{\color{red}x}e^{-3x}, since you have repeated roots.
    Ahhh! Tickle me with a feather lol, thanks alot man!
    Last edited by mr fantastic; November 26th 2009 at 03:26 AM.
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