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

Multiple Choice

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

A) $y = c _ { 1 } x ^ { - 1 } + c _ { 2 } x ^ { - 1 } \ln x$
B) $y = c _ { 1 } x ^ { - 1 } + c _ { 2 } x ^ { - 2 }$
C) $y = c _ { 1 } x ^ { ( - 3 + \sqrt { 5 } ) / 2 } + c _ { 2 } x ^ { ( - 3 - \sqrt { 5 } ) / 2 }$
D) $y = c _ { 1 } x + c _ { 2 } x \ln x$
E) $y = c _ { 1 } x + c _ { 2 } x ^ { 2 }$