Solve the Boundary-Value Problem, If Possible $$y ^ { tt } + 16 y ^ { t } + 64 y = 0 , y ( 0 ) = 0 , y ( 1 ) = 5$$

Multiple Choice

Solve the boundary-value problem, if possible. Select the correct answer.
$$y ^ { tt } + 16 y ^ { t } + 64 y = 0 , y ( 0 ) = 0 , y ( 1 ) = 5$$

A) $y ( x ) = 8 x e ^ { ( - 5 x + 5 ) }$
B) $y ( x ) = 5 e ^ { ( - 8 x - 8 ) }$
C) $y ( x ) = 5 x e ^ { ( - 8 x + 8 ) }$
D) $y ( x ) = 5 x e ^ { ( - 8 x - 8 ) }$
E) No solution