Laplace of cosh (sorry urgent)

Sep 2007
81
6
Hi all,

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

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

Cheers.
 

dwsmith

MHF Hall of Honor
Mar 2010
3,093
582
Florida
Hi all,

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

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

Cheers.
\(\displaystyle cosh=\frac{e^x+e^{-x}}{2}\)
 

chisigma

MHF Hall of Honor
Mar 2009
2,162
994
near Piacenza (Italy)
Is...

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

... so that...

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

Kind regards

\(\displaystyle \chi\) \(\displaystyle \sigma\)