The Solution Of $y ^ { \prime \prime } - n ^ { 2 } n ^ { 2 } y = 0 , y ( 0 ) = 0 , y ( 1 ) = 0 , n = 1,2,3 \ldots$

Multiple Choice

The solution of $y ^ { \prime \prime } - n ^ { 2 } n ^ { 2 } y = 0 , y ( 0 ) = 0 , y ( 1 ) = 0 , n = 1,2,3 \ldots$ is

A) $y = 0$
B) $y = c \cdot \sin ( n \pi x )$
C) $y = c \cdot \cos ( n \pi x )$
D) $c \left( e ^ { n xt } - e ^ { - nxt } \right)$
E) $c \left( e ^ { n xt } + e ^ { - nxt } \right)$