The Solution of the Differential Equation $x ^ { 2 } y ^ { \prime \prime } - 5 x y ^ { \prime } + 5 y = 0$

Multiple Choice

The solution of the differential equation $x ^ { 2 } y ^ { \prime \prime } - 5 x y ^ { \prime } + 5 y = 0$ is

A) $y = c _ { 1 } x + c _ { 2 } x ^ { 5 }$
B) $y = c _ { 1 } x ^ { 2 } \cos ( \ln x ) + c _ { 2 } x ^ { 2 } \sin ( \ln x )$
C) $y = c _ { 1 } x \cos ( 2 \ln x ) + c _ { 2 } x \sin ( 2 \ln x )$
D) $y = c _ { 1 } x ^ { ( 5 + \sqrt { 5 } ) / 2 } + c _ { 2 } x ^ { ( 5 - \sqrt { 5 } ) / 2 }$
E) $y = c _ { 1 } e ^ { 2 x } \cos x + c _ { 2 } x e ^ { 2 x } \sin x$