0006.tex

\begin{exerciseStatement}


 Compute the Laplace transform \(\mathcal{L}\{y\}\) of \(y =  -2 \, \delta\left(t - 4\right) + 3 \, e^{\left(2 \, t\right)} + 2 \, \mathrm{u}\left(t - 5\right) \) by using a transform table. 



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


\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[
\mathcal{L}\{y\} =  \frac{2 \, e^{\left(-5 \, s\right)}}{s} + \frac{3}{s - 2} - 2 \, e^{\left(-4 \, s\right)} \]
\end{exerciseAnswer}