The Eigenvalue Problem $y ^ { \prime \prime } + \lambda y = 0 , y ( 0 ) = 0 , y ( 1 ) = 0$

question 40

Multiple Choice

The eigenvalue problem $y ^ { \prime \prime } + \lambda y = 0 , y ( 0 ) = 0 , y ( 1 ) = 0$ has the solution

• A) \(y = \sin ( n \pi x ) , \lambda = ( n \pi ) ^ { 2 } , n = 1,2,3 , \ldots\)
• B) \(y = \cos ( n \pi x ) , \lambda = ( n \pi ) ^ { 2 } , n = 1,2,3 , \ldots\)
• C) \(y = \sin ( n \pi x ) , \lambda = n \pi , n = 1,2,3 , \ldots\)
• D) \(y = \cos ( n \pi x ) , \lambda = n \pi , n = 1,2,3 , \ldots\)
• E) none of the above

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