Solve the Differential Equation $$y ^ {tt } - 8 y ^ { t } + 41 y = 0$$

Multiple Choice

Solve the differential equation. Select the correct answer.
$$y ^ {tt } - 8 y ^ { t } + 41 y = 0$$

A) $y ( x ) = e ^ { 4 x } \left( c _ { 1 } \cos ( 5 x ) + c _ { 2 } x \sin ( 5 x ) \right)$
B) $y ( x ) = e ^ { 4 x } \left( c _ { 1 } \cos ( 5 x ) + c _ { 2 } \sin ( 5 x ) \right)$
C) $y ( x ) = e ^ { 5 x } \left( c _ { 1 } \cos ( 4 x ) + c _ { 2 } \sin ( 4 x ) \right)$
D) $y ( x ) = c e ^ { 4 x } \cos ( 5 x )$
E) $y ( x ) = e ^ { 4 x } \left( c _ { 1 } \cos ( 4 x ) + c _ { 2 } x \sin ( 4 x ) \right)$