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Math Help - One more Laplace/initial value question for class tomorrow!!!

  1. #1
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    One more Laplace/initial value question for class tomorrow!!!

    Solve the given initial value problem by Laplace transforms. Show te details of your work.

    y" - 2y' + 2y = 8e^(-t)(cos t) ; y(0) = 16; y'(0) = 16


    I have some of the problem done, but I am not sure that I am doing it right. I am supposed to present this at 1pm tomorrow during class, so any help before then would be greatly appreciated.
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  2. #2
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    Quote Originally Posted by Hollysti View Post
    Solve the given initial value problem by Laplace transforms. Show te details of your work.

    y" - 2y' + 2y = 8e^(-t)(cos t) ; y(0) = 16; y'(0) = 16


    I have some of the problem done, but I am not sure that I am doing it right. I am supposed to present this at 1pm tomorrow during class, so any help before then would be greatly appreciated.
    Take the Laplace transform of the equation:

    s^2 Y(s) -sy(0) - y'(0) -2[s Y(s) - y(0)] + 2Y(s) = 8 (s+1)/[(s+1)^2+1]

    (s^2 -2s +2)Y(s) = 8 (s+1)/[(s+1)^2+1] + 16s - 16

    So (if I have done this right)

    Y(s) = 8(2s^3 + 2s^2 + s - 3)/[(s^2 + 2s + 2)(s^2 - 2s + 2)].

    To finish this expand the left hand side in partial fractions and look up the
    corresponding inverse LTs to get the solution.

    RonL
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