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Math Help - second order differential constant coefficients homogeneous

  1. #1
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    second order differential constant coefficients homogeneous

    Hello

    I got the Roots R=5,2 for y''-7y'+10y=0

    So the equation would be y=C1e^5x +C2e^2x

    and not y=C1e^2x+C2e^5x OR Does It even matter where you stick the roots????



    THanks
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by andrewsx View Post
    Hello

    I got the Roots R=5,2 for y''-7y'+10y=0

    So the equation would be y=C1e^5x +C2e^2x

    and not y=C1e^2x+C2e^5x OR Does It even matter where you stick the roots????



    THanks
    The order of the coefficients doesn't matter.

    You can try it out both ways and see that you'll get the same thing if it was y_p=C_1e^{2x}+C_2e^{5x} or y_p=C_1e^{5x}+C_2e^{2x}

    However, note that C_1 and C_2 values you will get from solving it both ways will be different, but you will see that they correspond to the same e term.

    --Chris
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