Compute the Laplace transform \(\mathcal{L}\{y\}\) of \(y = -3 \, \delta\left(t - 1\right) + 2 \, e^{\left(4 \, t\right)} + 2 \, \mathrm{u}\left(t - 5\right) \) by using a transform table.
Then show how the integral definition of the Laplace transform to obtains same result.
Answer:
\[ \mathcal{L}\{y\} = \frac{2 \, e^{\left(-5 \, s\right)}}{s} + \frac{2}{s - 4} - 3 \, e^{\left(-s\right)} \]