Solve the Boundary-Value Problem, If Possible $y ^ { \prime \prime } + 16 y ^ { \prime } + 64 y = 0 , y ( 0 ) = 0 , y ( 1 ) = 4$

Multiple Choice

Solve the boundary-value problem, if possible. $y ^ { \prime \prime } + 16 y ^ { \prime } + 64 y = 0 , y ( 0 ) = 0 , y ( 1 ) = 4$

A) $y ( x ) = 4 x e ^ { ( - 8 x + 8 ) }$
B) $y ( x ) = 4 e ^ { ( - 8 x - 8 ) }$
C) $y ( x ) = 4 x e ^ { ( - 8 x - 8 ) }$
D) $y ( x ) = 8 x e ^ { ( - 4 x + 4 ) }$
E) No solution