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

question 11

Multiple Choice

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

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

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Definitions:

Favorable Spending Variance

A situation where the actual spending is less than the budgeted or expected amount.

Indirect Materials

Small items of material such as glue and nails that may be an integral part of a finished product, but whose costs cannot be easily or conveniently traced to it.

Flexible Budget

A budget that varies or adapts based on fluctuations in activity or volume levels.

Indirect Materials Cost

The cost of materials used in the production process that cannot be directly traced to the product, such as lubricants and cleaning supplies.