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

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

A) $y = c _ { 1 } x \cos ( \ln x ) + c _ { 2 } x \sin ( \ln x )$
B) $y = c _ { 1 } x ^ { 1 / 2 } \cos ( \sqrt { 3 } \ln x / 2 ) + c _ { 2 } x ^ { 1 / 2 } \sin ( \sqrt { 3 } \ln x / 2 )$
C) $y = c _ { 1 } x ^ { ( 1 + \sqrt { 3 } ) / 2 } + c _ { 2 } x ^ { ( 1 - \sqrt { 3 } ) / 2 }$
D) $y = c _ { 1 } x + c _ { 2 } x \ln x$
E) $y = c _ { 1 } x + c _ { 2 } x ^ { 2 }$

Correct Answer:

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