Solve the Initial-Value Problem $y ^ { tt } + 8 y ^ {t } + 41 y = 0 , y ( 0 ) = 1 , y ^ { \prime } ( 0 ) = 5$

Multiple Choice

Solve the initial-value problem.
$y ^ { tt } + 8 y ^ {t } + 41 y = 0 , y ( 0 ) = 1 , y ^ { \prime } ( 0 ) = 5$

A)
$y = e ^ { 5 x } \left( \cos ( 5 x ) + \frac { 9 } { 5 } \sin ( 5 x ) \right)$
B)
$y = e ^ { 4 x } \left( \cos ( 5 x ) - \frac { 2 } { 5 } \sin ( 5 x ) \right)$
C)
$y = e ^ { - 4 x } \left( \cos ( 5 x ) + \frac { 9 } { 5 } \sin ( 5 x ) \right)$
D)
$y = e ^ { - 5 x } \left( \cos ( 5 x ) + \frac { 2 } { 5 } \sin ( 5 x ) \right)$
E)
$y = e ^ { 5 x } \left( \cos ( 4 x ) + \frac { 9 } { 5 } \sin ( 4 x ) \right)$