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

question 18

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)\(y = e ^ { - 5 x } \left( \cos ( 5 x ) + \frac { 2 } { 5 } \sin ( 5 x ) \right)\)

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