The Solution of the Differential Equation $x ^ { 2 } y ^ { \prime \prime } - 3 x y ^ { \prime } + 4 y = 0$

The solution of the differential equation $x ^ { 2 } y ^ { \prime \prime } - 3 x y ^ { \prime } + 4 y = 0$ is

A) $y = c _ { 1 } x + c _ { 2 } x ^ { 2 }$
B) $y = c _ { 1 } x + c _ { 2 } x ^ { 3 }$
C) $y = c _ { 1 } x ^ { ( 3 + \sqrt { 7 } ) / 2 } + c _ { 2 } x ^ { ( 3 - \sqrt { 7 } ) / 2 }$
D) $y = c _ { 1 } x ^ { 2 } + c _ { 2 } x ^ { 2 } \ln x$
E) $y = c _ { 1 } x + c _ { 2 } x \ln x$

Correct Answer:

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