Compute the Laplace transform \(\mathcal{L}\{y\}\) of \(y = -2 \, \delta\left(t - 3\right) - 4 \, e^{\left(4 \, t\right)} - 3 \, \mathrm{u}\left(t - 1\right) \) by using a transform table.
Then show how the integral definition of the Laplace transform to obtains same result.
Answer:
\[ \mathcal{L}\{y\} = -\frac{3 \, e^{\left(-s\right)}}{s} - \frac{4}{s - 4} - 2 \, e^{\left(-3 \, s\right)} \]