Two Linearly Independent Solutions of the Differential Equation $y ^ { \prime \prime } - 4 y ^ { \prime } + 5 y = 0$

Two linearly independent solutions of the differential equation $y ^ { \prime \prime } - 4 y ^ { \prime } + 5 y = 0$ are

A) $y _ { 1 } = e ^ { x } , y _ { 2 } = e ^ { 5 x }$
B) $y _ { 1 } = e ^ { - x } , y _ { 2 } = e ^ { - 5 x }$
C) $y _ { 1 } = e ^ { 2 x } \cos x , y _ { 2 } = e ^ { 2 x } \sin x$
D) $y _ { 1 } = e ^ { x } \cos ( 2 x ) , y _ { 2 } = e ^ { x } \sin ( 2 x )$
E) $y _ { 1 } = e ^ { - x } \cos ( 2 x ) , y _ { 2 } = e ^ { - 2 x } \sin ( 2 x )$

Correct Answer:

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