Chapter 7.1, Problem 19P

Program Plan Intro

Program Description: Purpose of the problem is to obtain the Laplace transform of the given function $f\left(t\right)={\left(1+t\right)}^3$ .

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

  $\begin{array}{c}L\left\{t^n\right\}=\frac{n!}{s^{n+1}}\\ L\left\{1\right\}=\frac{1}{s}\end{array}$

Here, the value of $s>0$ and $n\ge 0$ .

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

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