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