Question

Determine the laplace transfrom of cosh3x

Answer 1

Hey reeny! Welcome to OpenStudy!\[\Large\rm \mathscr L\{\cosh3x\}=\frac{1}{2}\mathscr L\{e^{3x}+e^{-3x}\}\]

\[\Large\rm =\frac{1}{2}\mathscr L\{e^{3x}\}+\frac{1}{2}\mathscr L\{e^{-3x}\}\]

Answer 2

Remember how to Laplace exponential functions? :)
Just had to remember your identity for Cosh.

Answer 3

This is the identity I'm talking about, just in case there is any confusion.
\[\Large\rm \color{royalblue}{\cosh x=\frac{1}{2}(e^{x}+e^{-x})}\]

Answer 4

The trick here is to recall the definition of the hyperbolic cosine, which zepdrix has just done, and then to focus on finding the Laplace transform of each of the exponential functions separately. Due to the linearity of the Laplace transform, you can then add together the two resulting Laplace transforms. Finally, you multiply the resulting sum by that (1/2).

This approach makes more sense (to me at least) than does memorizing the Laplace transform of the hyperbolic trig functions.