<exercise masterit-seed="6682" masterit-slug="D2" masterit-name="Laplace transforms from formula and definition">
<statement>
<p>
Compute the Laplace transform <m>\mathcal{L}\{y\}</m> of
<m>y = 2 \, \delta\left(t - 1\right) - 5 \, e^{\left(4 \, t\right)} - 4 \, \mathrm{u}\left(t - 2\right) </m> by using a transform table.
</p>
<p>
Then show how the integral definition of the Laplace transform
to obtains same result.
</p>
</statement>
<answer>
<me>
\mathcal{L}\{y\} = -\frac{4 \, e^{\left(-2 \, s\right)}}{s} - \frac{5}{s - 4} + 2 \, e^{\left(-s\right)} </me>
</answer>
</exercise>
