<exercise masterit-seed="9392" 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 = 5 \, \delta\left(t - 3\right) + 2 \, e^{\left(2 \, t\right)} - 3 \, \mathrm{u}\left(t - 5\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{3 \, e^{\left(-5 \, s\right)}}{s} + \frac{2}{s - 2} + 5 \, e^{\left(-3 \, s\right)} </me>
</answer>
</exercise>
