GATE EC 2013 Set 1 Q36 — Differential Equations

A system is described by the differential equation $\dfrac{\mathrm{d}^{2} y}{\mathrm{d} x} + 5\dfrac{\mathrm{d}y }{\mathrm{d} x} + 6y(t) = x(t).$

Let $x(t)$ be a rectangular pulse given by

$x(t) = \begin{cases} 1&0<t<2 \\ 0&\text{otherwise} \end{cases}$

Assuming that $y(0) = 0$ and $\dfrac{\mathrm{d}y }{\mathrm{d} x} = 0$ at $t=0,$ the Laplace transform of $y(t)$ is