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