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

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) $y = e ^ { 4 x } \left( \cos ( 5 x ) - \frac { 2 } { 5 } \sin ( 5 x ) \right)$

Correct Answer:

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