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

question 30

Multiple Choice

The general 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) \(c \left( e ^ { n + x } - e ^ { - n + x } \right)\)
• E) \(c \left( e ^ { n + x } + e ^ { - n + x } \right)\)

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