In the Previous Problem, Apply the Laplace Transform $U ( x , s ) = \mathcal { L } \{ u ( x , t ) \}$

In the previous problem, apply the Laplace transform. The resulting equation for $U ( x , s ) = \mathcal { L } \{ u ( x , t ) \}$ is

A) $a ^ { 2 } \frac { \partial ^ { 2 } U } { \partial x ^ { 2 } } + s ^ { 2 } U = - s f ( x )$
B) $a ^ { 2 } \frac { \partial ^ { 2 } U } { \partial x ^ { 2 } } + s ^ { 2 } U = 0$
C) $a ^ { 2 } \frac { \partial ^ { 2 } U } { \partial x ^ { 2 } } - s ^ { 2 } U = - f ( x )$
D) $a ^ { 2 } \frac { \partial ^ { 2 } U } { \partial x ^ { 2 } } - s ^ { 2 } U = s f ( x )$
E) $a ^ { 2 } \frac { \partial ^ { 2 } U } { \partial x ^ { 2 } } - s ^ { 2 } U = 0$