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Math Help - Euler Cauchy 3rd Order Linear DE

  1. #1
    Member zangestu888's Avatar
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    Euler Cauchy 3rd Order Linear DE

    x^3y'''-x^2y''+2xy'-2y=0

    That is the Given ODE, am not sure how to find the characterstic polynomial please if anyone could guide me on how to do that? my guess from reading and checking websites i got.

    m^3-4m^2+5m-2=0
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by zangestu888 View Post
    x^3y'''-x^2y''+2xy'-2y=0

    That is the Given ODE, am not sure how to find the characterstic polynomial please if anyone could guide me on how to do that? my guess from reading and checking websites i got.

    m^3-4m^2+5m-2=0
    Use a trial solution y=x^m which then gives:

     <br />
m(m-1)(m-2)-m(m-1)+2m-2=0<br />

    which simplifies to your cubic.

    CB
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