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

question 27

Multiple Choice

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

• A) \(\lambda = n \pi , y = \cos ( n \pi x ) , n = 0,1,2 , \ldots\)
• B) \(\lambda = n \pi , y = \sin ( n \pi x ) , n = 1,2,3 , \ldots\)
• C) \(\lambda = n ^ { 2 } \pi ^ { 2 } , y = \cos ( n \pi x ) , n = 0,1,2 , \ldots\)
• D) \(\lambda = n ^ { 2 } \pi ^ { 2 } , y = \sin ( n \pi x ) , n = 1,2,3 , \ldots\)
• E) \(\lambda = n \pi , y = \cos ( n \pi x ) + \sin ( n \pi x ) , n = 1,2,3 , \ldots\)

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Definitions:

Low Birthweight

Refers to a birth weight of a newborn less than 2,500 grams (5 pounds, 8 ounces), which may be linked to health issues.

Brain Development

The process of growth and change in the brain’s structure, function, and pathways that occurs throughout a person’s life, but is most intense during childhood.

Selective Attrition

The phenomenon where participants drop out of a study over time, potentially leading to biased results if the dropout rate varies among the groups being studied.

Longitudinal Research

involves studies conducted over a lengthy period, allowing researchers to observe developments or changes in the subjects over time.