When the Laplace Transform Is Applied to the Problem $y ^ { \prime \prime } + 2 y ^ { \prime } + y = e ^ { 3 t } , y ( 0 ) = 1 , y ^ { \prime } ( 0 ) = 2$

Multiple Choice

When the Laplace transform is applied to the problem $y ^ { \prime \prime } + 2 y ^ { \prime } + y = e ^ { 3 t } , y ( 0 ) = 1 , y ^ { \prime } ( 0 ) = 2$ the resulting transformed equation is

A) $\left( s ^ { 2 } + 2 s + 1 \right) Y = - s - 4 + 1 / ( s - 3 )$
B) $\left( s ^ { 2 } + 2 s + 1 \right) Y = s - 4 + 1 / ( s - 3 )$
C) $\left( s ^ { 2 } + 2 s + 1 \right) Y = s + 4 + 1 / ( s + 3 )$
D) $\left( s ^ { 2 } + 2 s + 1 \right) Y = - s - 4 + 1 / ( s + 3 )$
E) $\left( s ^ { 2 } + 2 s + 1 \right) Y = s + 4 + 1 / ( s - 3 )$