Solve the Initial-Value Problem $y ^ { \prime \prime } + 8 y ^ { \prime } + 41 y = 0 , y ( 0 ) = 1 , y ^ { \prime } ( 0 ) = 7$

question 44

Multiple Choice

Solve the initial-value problem. $y ^ { \prime \prime } + 8 y ^ { \prime } + 41 y = 0 , y ( 0 ) = 1 , y ^ { \prime } ( 0 ) = 7$

• A) \(y = e ^ { 5 x } \left( \cos ( 5 x ) + \frac { 11 } { 5 } \sin ( 5 x ) \right)\)
• B) \(y = e ^ { - 5 x } \left( \cos ( 5 x ) + \frac { 2 } { 5 } \sin ( 5 x ) \right)\)
• C) \(y = e ^ { 5 x } \left( \cos ( 4 x ) + \frac { 11 } { 5 } \sin ( 4 x ) \right)\)
• D) \(y = e ^ { - 4 x } \left( \cos ( 5 x ) + \frac { 11 } { 5 } \sin ( 5 x ) \right)\)
• E) \(y = e ^ { 4 x } \left( \cos ( 5 x ) - \frac { 2 } { 5 } \sin ( 5 x ) \right)\)

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Definitions:

Cash

A form of liquid asset that includes physical currency such as banknotes and coins, and demand deposits that can be quickly converted into physical cash.

Incremental Value

The additional or extra value generated by undertaking a new project, making an investment, or initiating a new action.

Equity-Financed

A method of raising capital through the sale of shares in the company, leading to shareholder ownership.

Firm A

A placeholder name often used to refer to a specific company in examples or case studies.