Compute the Laplace transform \(\mathcal{L}\{y\}\) of \(y = -3 \, \delta\left(t - 5\right) + 3 \, e^{\left(3 \, t\right)} + 4 \, \mathrm{u}\left(t - 1\right) \) by using a transform table.
Then show how the integral definition of the Laplace transform to obtains same result.
Answer:
\[ \mathcal{L}\{y\} = \frac{4 \, e^{\left(-s\right)}}{s} + \frac{3}{s - 3} - 3 \, e^{\left(-5 \, s\right)} \]