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Math Help - Inverse Laplace Transform

  1. #1
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    Inverse Laplace Transform

    Find the IVL of \frac{(s-2)e^{-s}}{s^2-4s+3}.

    I am not understanding how my textbook gets the answer u_1(t)e^{2(t-1)}cosh(t-1)

    I end up with

    e^{-s}\left(\frac{1}{2(s-1)}+\frac{1}{2(s-3)}\right)

    =u_1(t)\left(\frac{1}{2}e^{(t-1)}+\frac{1}{2}e^{3(t-1)}\right)
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  2. #2
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    Quote Originally Posted by petition Edgecombe View Post
    Find the IVL of \frac{(s-2)e^{-s}}{s^2-4s+3}.

    I am not understanding how my textbook gets the answer u_1(t)e^{2(t-1)}cosh(t-1)

    I end up with

    e^{-s}\left(\frac{1}{2(s-1)}+\frac{1}{2(s-3)}\right)

    =u_1(t)\left(\frac{1}{2}e^{(t-1)}+\frac{1}{2}e^{3(t-1)}\right)
    = u_1(t) e^{2(t-1)} \left(\frac{1}{2}e^{-(t-1)}+\frac{1}{2}e^{(t-1)}\right) \, ....
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  3. #3
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    OK, so my answer wasn't wrong, it just wasn't simplified. I've got to remember my hyperbolic functions.
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