Solve the Initial-Value Problem $y ^ { tt } + 8 y ^ { t } + 41 y = 0 , y ( 0 ) = 1 , y ^ { t } ( 0 ) = 5$

question 42

Multiple Choice

Solve the initial-value problem. $y ^ { tt } + 8 y ^ { t } + 41 y = 0 , y ( 0 ) = 1 , y ^ { t } ( 0 ) = 5$

• A)
• \(y = e ^ { 5 x } \left( \cos ( 5 x ) + \frac { 9 } { 5 } \sin ( 5 x ) \right)\)
• B)
• \(y = e ^ { 4 x } \left( \cos ( 5 x ) - \frac { 2 } { 5 } \sin ( 5 x ) \right)\)
• C)
• \(y = e ^ { - 4 x } \left( \cos ( 5 x ) + \frac { 9 } { 5 } \sin ( 5 x ) \right)\)
• D)
• \(y = e ^ { - 5 x } \left( \cos ( 5 x ) + \frac { 2 } { 5 } \sin ( 5 x ) \right)\)
• E)
• \(y = e ^ { 5 x } \left( \cos ( 4 x ) + \frac { 9 } { 5 } \sin ( 4 x ) \right)\)

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Definitions:

Robert Merton

An influential American sociologist known for developing theories on social structure, anomie, and for the concept of self-fulfilling prophecy, among other contributions to sociology.

Societal Community

A group of people who share common values, traditions, and behaviors, forming a cohesive unit within a larger society.

Integrative

Approaches or methods that combine different theories, practices, or systems into a unified whole.

Imperative

A crucial or essential condition, requirement, or command that is binding and necessary.