Solve the Boundary-Value Problem, If Possible $$y ^ { tt } + 5 y ^ { t } - 14 y = 0 , y ( 0 ) = 0 , y ( 2 ) = 1$$

question 33

Multiple Choice

Solve the boundary-value problem, if possible. $$y ^ { tt } + 5 y ^ { t } - 14 y = 0 , y ( 0 ) = 0 , y ( 2 ) = 1$$

• A) \(y ( x ) = \left( e ^ { 4 } - e ^ { - 14 } \right) ^ { - 1 } \left( e ^ { 2 x } - e ^ { - 7 x } \right)\)
• B) \(y ( x ) = \left( e ^ { 2 } - e ^ { - 14 } \right) \left( e ^ { 2 x } - e ^ { - 7 x } \right)\)
• C) \(y ( x ) = \left( e ^ { 7 } - e ^ { - 14 } \right) ^ { - 1 } \left( e ^ { x } - e ^ { - 7 x } \right)\)
• D) \(y ( x ) = \left( e ^ { 2 } - e ^ { - 14 } \right) ^ { - 1 } \left( e ^ { 2 x } - e ^ { - 7 x } \right)\)
• E) No solution

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Definitions:

Demand Curve

A graph showing the relationship between the price of a good and the quantity of that good consumers are willing and able to purchase at different prices.

Water-Diamond Paradox

A paradox that questions why diamonds are expensive and water is cheap when water is essential for survival and diamonds are not.

Utility Theory

An economic theory that models how individuals make choices based on their preferences and the perceived utility or satisfaction from goods and services.

Marginal Utility

The additional satisfaction or benefit gained from consuming one more unit of a good or service.