The Solution of the Eigenvalue Problem $y ^ { \prime \prime } + \lambda y = 0 , y ( 0 ) = 0 , y ( 2 ) = 0$

question 16

Multiple Choice

The solution of the eigenvalue problem $y ^ { \prime \prime } + \lambda y = 0 , y ( 0 ) = 0 , y ( 2 ) = 0$ is

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

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Definitions:

Gain on Disposal

The financial profit made from selling or disposing of a fixed asset for more than its book value.

Accumulated Depreciation

The total depreciation expense charged for an asset since it was put into use, reflecting its loss of value over time.

Replacement Cost

The current cost of replacing an asset with a similar new asset, reflecting the current market conditions and prices.

Gain or Loss

Refers to the financial result of a transaction where assets exceed liabilities (gain) or liabilities exceed assets (loss).