A system is described by the differential equation $${{{d^2}y} \over {d{t^2}}} + 5{{dy} \over {dt}} + 6y\left( t \right) = x\left( t \right).$$     Let x(t) be a rectangular pulse given by
$$x\left( t \right) = \left\{ {\matrix{ {1,} & {0 < t < 2} \cr {0,} & {{\rm{otherwise}}} \cr } } \right.$$
Assuming that y(0) = 0 and $${{dy} \over {dt}} = 0$$  at t = 0, the Laplace transform of y(t) is

A. $${{{e^{ - 2s}}} \over {s\left( {s + 2} \right)\left( {s + 3} \right)}}$$

B. $${{1 - {e^{ - 2s}}} \over {s\left( {s + 2} \right)\left( {s + 3} \right)}}$$

C. $${{{e^{ - 2s}}} \over {\left( {s + 2} \right)\left( {s + 3} \right)}}$$

D. $${{1 - {e^{ - 2s}}} \over {\left( {s + 2} \right)\left( {s + 3} \right)}}$$

Answer: Option B