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Math Help - Homog. Lin. Eq's with Constant Coeff.

  1. #1
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    Homog. Lin. Eq's with Constant Coeff.

    Find the general sol'n of the given Dif EQ:

    1.) \frac{d^2y}{dt^2} - 10\frac{dy}{dt} + 25y = 0

    WORK:

    8y'' + 2y' - y = 0

    So our auxiliary eq. is 8m^2 + 2m - 1 = 0

    Factor: (2m + 1)(4m - 1) = 0,

    So m = -1/2, 1/4.

    Therefore, the gen. sol'n is:

    y = c_1e^{\frac{-t}{2}} + c_2e^{\frac{t}{4}}

    Is this right?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Ideasman View Post
    Find the general sol'n of the given Dif EQ:

    1.) \frac{d^2y}{dt^2} - 10\frac{dy}{dt} + 25y = 0

    WORK:

    8y'' + 2y' - y = 0

    So our auxiliary eq. is 8m^2 + 2m - 1 = 0

    Factor: (2m + 1)(4m - 1) = 0,

    So m = -1/2, 1/4.

    Therefore, the gen. sol'n is:

    y = c_1e^{\frac{-t}{2}} + c_2e^{\frac{t}{4}}

    Is this right?
    That is OK for the equation you are working on, but its not the equation you
    are asked to solve, which has a double root.

    RonL
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  3. #3
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    Quote Originally Posted by CaptainBlack View Post
    That is OK for the equation you are working on, but its not the equation you
    are asked to solve, which has a double root.

    RonL
    Ha, think I copied down the wrong one on here:

    It should have been 8y'' + 2y' - y = 0. Ok, so it's right if it was that ?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by Ideasman View Post
    Ha, think I copied down the wrong one on here:

    It should have been 8y'' + 2y' - y = 0. Ok, so it's right if it was that ?
    Yes

    RonL
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