0002.tex

\begin{exerciseStatement}


 Compute the Laplace transform \(\mathcal{L}\{y\}\) of \(y =  -2 \, \delta\left(t - 1\right) + 4 \, e^{\left(3 \, t\right)} - 2 \, \mathrm{u}\left(t - 2\right) \) by using a transform table. 



 Then show how the integral definition of the Laplace transform to obtains same result. 


\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[
\mathcal{L}\{y\} =  -\frac{2 \, e^{\left(-2 \, s\right)}}{s} + \frac{4}{s - 3} - 2 \, e^{\left(-s\right)} \]
\end{exerciseAnswer}