Using Laplace Transform Methods, the Solution Of $y ^ { \prime \prime } + y = \delta ( t - \pi / 2 ) , y ( 0 ) = 1$

Multiple Choice

Using Laplace transform methods, the solution of $y ^ { \prime \prime } + y = \delta ( t - \pi / 2 ) , y ( 0 ) = 1$ , $y ^ { \prime } ( 0 ) = 0$ is

A) $y = \sin t + \sin ( t - \pi / 2 ) u ( t - \pi / 2 )$
B) $y = \sin t - \cos ( t - \pi / 2 ) \boldsymbol { u } ( t - \pi / 2 )$
C) $y = \cos t + \sin ( t - \pi / 2 ) u ( t - \pi / 2 )$
D) $y = \cos t + \cos ( t - \pi / 2 ) \boldsymbol { u } ( t - \pi / 2 )$
E) $y = \cos t - \sin ( t - \pi / 2 ) u ( t - \pi / 2 )$