The function $x(t)$ satisfies the ODE
$\ddot{x} + 6\dot{x} + 9x = \phi$
with initial conditions $x(0) = 0$, $\dot{x}(0) = 0$ and
$\phi = \begin{cases} 3, & 0 \le t \le 3, \\ 0, & t > 3. \end{cases}$
(a)
Find the Laplace Transform $X(s)$ of $x(t)$.
$X(s) = \frac{3(1 - e^{-3s})}{s(s+3)^2}$
