Two Linearly Independent Solutions of the Differential Equation $y ^ { \prime \prime } - 6 y ^ { \prime } + 9 y = 0$

Multiple Choice

Two linearly independent solutions of the differential equation $y ^ { \prime \prime } - 6 y ^ { \prime } + 9 y = 0$ are

A) $y _ { 1 } = e ^ { 3 x } , y _ { 2 } = x e ^ { 3 x }$
B) $y _ { 1 } = e ^ { - 3 x } , y _ { 2 } = x e ^ { - 3 x }$
C) $y _ { 1 } = e ^ { 3 x } , y _ { 2 } = x e ^ { - 3 x }$
D) $y _ { 1 } = e ^ { 3 x } \cos ( x ) , y _ { 2 } = x e ^ { 3 x } \sin ( x )$
E) $y _ { 1 } = e ^ { - 3 x } \cos ( 3 x ) , y _ { 2 } = e ^ { - 3 x } \sin ( x )$