Solve the Initial-Value Problem $$y ^ { tt } + 8 y ^ { t } + 41 y = 0 , y ( 0 ) = 1 , y ^ { t} ( 0 ) = 2$$

question 139

Multiple Choice

Solve the initial-value problem.
$$y ^ { tt } + 8 y ^ { t } + 41 y = 0 , y ( 0 ) = 1 , y ^ { t} ( 0 ) = 2$$

• A)
• \[y = e ^ { 5 x } \left( \cos ( 5 x ) + \frac { 6 } { 5 } \sin ( 5 x ) \right)\]
• B)
• \[y = e ^ { - 4 x } \left( \cos ( 5 x ) + \frac { 6 } { 5 } \sin ( 5 x ) \right)\]
• C)
• \[y = e ^ { 5 x } \left( \cos ( 4 x ) + \frac { 6 } { 5 } \sin ( 4 x ) \right)\]
• D)
• \[y = e ^ { 4 x } \left( \cos ( 5 x ) - \frac { 2 } { 5 } \sin ( 5 x ) \right)\]
• E)
• \[y = e ^ { - 5 x } \left( \cos ( 5 x ) + \frac { 2 } { 5 } \sin ( 5 x ) \right)\]

---

Definitions:

Cardiac Disease

A wide range of conditions affecting the heart's structure and function, such as coronary artery disease or arrhythmias.

Betty Neuman

A nursing theorist known for developing the Neuman Systems Model, which focuses on the response of patients to potential or actual environmental stressors.

Health Risk Factors

Aspects of personal behavior or lifestyle, environmental exposure, or genetic susceptibility that increase the likelihood of developing a disease.

Behavior Changes

Modifications or transformations in actions or conduct, often in response to internal or environmental factors, medical conditions, or therapy.