Chapter 6.2, Problem 39P

(a)

To determine

To show: The coefficient is $A_k=\frac{P\left(r_k\right)}{Q^{\prime }\left(r_k\right)},k=1,\mathrm{...},n$.

(b)

To determine

To show: The inverse Laplace transform of F is given as $L^{-1}\left\{F\left(s\right)\right\}={\displaystyle \sum _{k=1}^n\frac{P\left(r_k\right)}{Q^{\prime }\left(r_k\right)}{e}^{r_{k}t}}$.