Solve the Initial-Value Problem $y ^ { \prime \prime } - 2 y ^ { \prime } - 24 y = 0 , y ( 1 ) = 4 , y ^ { \prime } ( 1 ) = 5$

question 20

Multiple Choice

Solve the initial-value problem. $y ^ { \prime \prime } - 2 y ^ { \prime } - 24 y = 0 , y ( 1 ) = 4 , y ^ { \prime } ( 1 ) = 5$ .

• A) \(y ( x ) = \frac { 1 } { 10 } e ^ { 4 ( x - 1 ) } + \frac { 1 } { 23 } e ^ { - 6 ( x - 1 ) }\)
• B) \(y ( x ) = \frac { 1 } { 10 } e ^ { 4 x } - \frac { 1 } { 23 } e ^ { - 6 x }\)
• C) \(y ( x ) = e ^ { 6 x } - e ^ { - 4 x }\)
• D) \(y ( x ) = \frac { 21 } { 10 } e ^ { 6 ( x - 1 ) } + \frac { 19 } { 10 } e ^ { - 4 ( x - 1 ) }\)
• E) \(y ( x ) = \frac { 1 } { 10 } e ^ { x } - \frac { 1 } { 23 } e ^ { - x }\)

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Definitions:

Profit-maximizing

The method of modifying manufacturing and selling tactics to obtain the maximum profit achievable.

Marginal Revenue

The extra revenue earned by selling an additional unit of a product or service.

Marginal Cost

Refers to the increase in total production cost that comes from making or producing one additional unit.

Increased By

A mathematical operation indicating that a certain value should be added to another value, resulting in a larger amount.