0003.tex

\begin{exerciseStatement}


 Explain how to use convolution along with the formula \(\mathcal{L}\{e^{at})=\frac{1}{s-a}\)to find the following inverse Laplace transform: 

\[
          \mathcal{L}^{-1}\left\{ \frac{3}{5 \, {\left(s + 7\right)} {\left(s - 4\right)}} \right\}
      \]
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[ \frac{3}{55} \, e^{\left(4 \, t\right)} - \frac{3}{55} \, e^{\left(-7 \, t\right)} \]
\end{exerciseAnswer}