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Math Help - Laplace of cosh (sorry urgent)

  1. #1
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    Laplace of cosh (sorry urgent)

    Hi all,

    Sorry I hate posting urgent questions up here but either way I need some help.

    I'm looking for the laplace of \cosh^2{t} but I've got no idea how to go about it, can anyone help out?

    Cheers.
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  2. #2
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    Quote Originally Posted by Peleus View Post
    Hi all,

    Sorry I hate posting urgent questions up here but either way I need some help.

    I'm looking for the laplace of \cosh^2{t} but I've got no idea how to go about it, can anyone help out?

    Cheers.
    cosh=\frac{e^x+e^{-x}}{2}
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  3. #3
    MHF Contributor chisigma's Avatar
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    Is...

    \cosh^{2} t = \frac{1}{2} + \frac{e^{2t} + e^{-2t}}{4} (1)

    ... so that...

    \mathcal{L} \{\cosh^{2} t\} = \frac{1}{2s} + \frac{1}{4(s-2)} + \frac{1}{4(s+2)} (2)

    Kind regards

    \chi \sigma
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