0006.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: 

\[
          \mathcal{L}^{-1}\left\{ \frac{3}{2 \, {\left(s + 6\right)} {\left(s + 2\right)}} \right\}
      \]
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[ \frac{3}{8} \, e^{\left(-2 \, t\right)} - \frac{3}{8} \, e^{\left(-6 \, t\right)} \]
\end{exerciseAnswer}