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Math Help - Help with Third-order linear ordinary differential equation

  1. #1
    cYn
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    Help with Third-order linear ordinary differential equation

    OK here is my problem:

    y''' - y'' - 2y' = 0

    And these are my steps

    m^3 - m^2 - 2m = 0
    m(m^2 - m - 2) = 0
    m(m + 1)(m - 2) = 0
    m = -1, 0, 2


    *C1, C2, C3 = Csub1, Csub2, Csub3

    y = C1e^0x + C2e^2x + C3e^-x
    solution: y = C1 + C2e^2x + C3e^-x

    but when checking the problem on Wolfram Alpha, the solution is:

    y = C1 + (1/2)C2e^2x + C3(-e^-x)

    Is there a step I'm missing?
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  2. #2
    MHF Contributor
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    Quote Originally Posted by cYn View Post
    OK here is my problem:

    y''' - y'' - 2y' = 0

    And these are my steps

    m^3 - m^2 - 2m = 0
    m(m^2 - m - 2) = 0
    m(m + 1)(m - 2) = 0
    m = -1, 0, 2


    *C1, C2, C3 = Csub1, Csub2, Csub3

    y = C1e^0x + C2e^2x + C3e^-x
    solution: y = C1 + C2e^2x + C3e^-x

    but when checking the problem on Wolfram Alpha, the solution is:

    y = C1 + (1/2)C2e^2x + C3(-e^-x)

    Is there a step I'm missing?
    These answers are the same. It might help if you choose different constant names like

    y = k_1 + k_2 e^{2x} + k_3 e^{-x}

    so you can choose your constants to recover Wolfram's.
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  3. #3
    cYn
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    Quote Originally Posted by Danny View Post
    These answers are the same. It might help if you choose different constant names like

    y = k_1 + k_2 e^{2x} + k_3 e^{-x}

    so you can choose your constants to recover Wolfram's.
    Ahh, thank you.
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