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Math Help - Laplace transforms

  1. #1
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    Laplace transforms

    Solve the initial value problem by laplace transforms:
    y" - 4y' - 5y = 2 + e^(-t); y(0) = y'(0) = 0.

    I have the first couple steps done, but I keep getting stuck, so if someone would help me with this problem I would appreciate it. It is on the review for my final and I think there will be one like it on the test, so if you could go into detailed explaination and show every step, maybe I will be able to do the problem on the final. Thank you.
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  2. #2
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    You do the last step
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  3. #3
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    Would you be able to tell me how you got the first step of the problem? I would have been able to work the problem, I think, but I didn't know where to start. Also, are you sure that the partial derivatives towards the bottom are correct, because I am getting different answers for them. Thank you.
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  4. #4
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    Quote Originally Posted by Hollysti View Post
    Would you be able to tell me how you got the first step of the problem? I would have been able to work the problem, I think, but I didn't know where to start. Also, are you sure that the partial derivatives towards the bottom are correct, because I am getting different answers for them. Thank you.
    You are supposed to know that:

    Lf''(s) = s^2 Lf(s) - s f'(0) - f(0)

    and that:

    Lf'(s) = s Lf(s) - f(0)

    Lf(s) = 1/s when f(t) = 1 for all t

    Lf(s) = 1/(s-a) when f(t)=e^(at)

    Then you assemble these into:

    s^2 Lf(s) - s f'(0) - f(0) -4[s Lf(s) - f(0)] -5 Lf(s) = 2/s + 1/(s+1)

    Putting Lf = F, and using the initial conditions this becomes:

    s^2 F(s) - 4 s F(s) - 5 F(s) = 2/s + 1/(s+1)

    RonL
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