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

question 14

Multiple Choice

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

• 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:

Fluid Overload

A condition where there is an excessive accumulation of fluid in the body, often leading to swelling and various health complications.

Pulmonary Hypertension

A type of high blood pressure that affects the arteries in the lungs and the right side of the heart, potentially leading to various symptoms and complications.

Conversational Dyspnea

Difficulty in breathing that occurs during conversation, indicating breathing distress or disorders.

Right-sided Heart Failure

A condition where the right ventricle of the heart is unable to pump blood effectively to the lungs, leading to fluid buildup and congestion.