Solve the Boundary-Value Problem, If Possible $$y ^ { tt } + 16 y ^ { t } + 64 y = 0 , y ( 0 ) = 0 , y ( 1 ) = 5$$

question 64

Multiple Choice

Solve the boundary-value problem, if possible. Select the correct answer.
$$y ^ { tt } + 16 y ^ { t } + 64 y = 0 , y ( 0 ) = 0 , y ( 1 ) = 5$$

• A) \(y ( x ) = 8 x e ^ { ( - 5 x + 5 ) }\)
• B) \(y ( x ) = 5 e ^ { ( - 8 x - 8 ) }\)
• C) \(y ( x ) = 5 x e ^ { ( - 8 x + 8 ) }\)
• D) \(y ( x ) = 5 x e ^ { ( - 8 x - 8 ) }\)
• E) No solution

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Definitions:

Efficient Output Level

The quantity of output at which a firm's average total cost is minimized.

Units

Basic quantities or measurements used as a standard to express the amount, level, or size of something.

Monopolistic Competitor

A market structure in which many companies sell products or services that are similar but not identical, allowing for some degree of market power.

Perfect Competitor

A theoretical market structure where numerous small firms sell identical products, and no single seller can influence the market price.