Compute the Laplace transform \(\mathcal{L}\{y\}\) of \(y = -5 \, \delta\left(t - 3\right) + 4 \, e^{\left(2 \, t\right)} + 3 \, \mathrm{u}\left(t - 4\right) \) by using a transform table.
Then show how the integral definition of the Laplace transform to obtains same result.
Answer:
\[ \mathcal{L}\{y\} = \frac{3 \, e^{\left(-4 \, s\right)}}{s} + \frac{4}{s - 2} - 5 \, e^{\left(-3 \, s\right)} \]