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

Multiple Choice

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

A) $y _ { 1 } = e ^ { 2 x } , y _ { 2 } = e ^ { 2 x }$
B) $y _ { 1 } = e ^ { 2 x } , y _ { 2 } = x e ^ { 2 x }$
C) $y _ { 1 } = e ^ { 2 x } , y _ { 2 } = e ^ { - 2 x }$
D) $y _ { 1 } = e ^ { - 2 x } , y _ { 2 } = x e ^ { - 2 x }$
E) $y _ { 1 } = e ^ { - 2 x } , y _ { 2 } = x e ^ { 2 x }$