Solve the Initial-Value Problem $$y ^ { tt } + 8 y ^ { t} + 41 y = 0 , y ( 0 ) = 1 , y ^ { t } ( 0 ) = 4$$

question 82

Multiple Choice

Solve the initial-value problem. Select the correct answer.
$$y ^ { tt } + 8 y ^ { t} + 41 y = 0 , y ( 0 ) = 1 , y ^ { t } ( 0 ) = 4$$

• A)
• \[y = e ^ { - 4 x } \left( \cos ( 5 x ) + \frac { 8 } { 5 } \sin ( 5 x ) \right)\]
• B)
• \[y = e ^ { - 5 x } \left( \cos ( 5 x ) + \frac { 2 } { 5 } \sin ( 5 x ) \right)\]
• C)
• \[y = e ^ { 5 x } \left( \cos ( 4 x ) + \frac { 8 } { 5 } \sin ( 4 x ) \right)\]
• D)
• \[y = e ^ { 4 x } \left( \cos ( 5 x ) - \frac { 2 } { 5 } \sin ( 5 x ) \right)\]
• E)
• \[y = e ^ { 5 x } \left( \cos ( 5 x ) + \frac { 8 } { 5 } \sin ( 5 x ) \right)\]

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