Solve the Differential Equation $y ^ { \prime \prime } - 8 y ^ { \prime } + 25 y = 0$

Solve the differential equation. $y ^ { \prime \prime } - 8 y ^ { \prime } + 25 y = 0$

A) $y ( x ) = c e ^ { 4 x } \cos ( 3 x )$
B) $y ( x ) = e ^ { 4 x } \left( c _ { 1 } \cos ( 3 x ) + c _ { 2 } x \sin ( 3 x ) \right)$
C) $y ( x ) = e ^ { 4 x } \left( c _ { 1 } \cos ( 4 x ) + c _ { 2 } x \sin ( 4 x ) \right)$
D) $y ( x ) = e ^ { 3 x } \left( c _ { 1 } \cos ( 4 x ) + c _ { 2 } \sin ( 4 x ) \right)$
E) $y ( x ) = e ^ { 4 x } \left( c _ { 1 } \cos ( 3 x ) + c _ { 2 } \sin ( 3 x ) \right)$

Correct Answer:

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