Chapter 7.1, Problem 30P

Program Plan Intro

Program Description: Purpose of problem is to obtain the inverse Laplace transformation of given function $F\left(s\right)=\frac{9+s}{4-s^2}$ .

Summary introduction:Program will use the inverse of Laplace transform as given below.

  $\begin{array}{c}\cosh kt=L^{-1}\left\{\frac{s}{s^2-k^2}\right\}\\ \sinh kt=L^{-1}\left\{\frac{k}{s^2-k^2}\right\}\end{array}$

Here, the value of $s>\left|k\right|$ .

The linearity theorem of the Laplace transform for all $s$ such that the functions $f$ and $g$ both exists is defined as,

  $L\left\{af\left(t\right)+bg\left(t\right)\right\}=aL\left\{f\left(t\right)\right\}+bL\left\{g\left(t\right)\right\}$