Find the General Solution of the Differential Equation $x \frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 1 } { 2 y } \ln x$

Multiple Choice

Find the general solution of the differential equation. Solve for y as a function of x. $x \frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 1 } { 2 y } \ln x$

A) $y = \sqrt { \frac { \ln ^ { 2 } | x | + C } { 2 } }$
B) $y = \frac { \sqrt { \ln ^ { 2 } | x | + C } } { 2 }$
C) $y = \sqrt { \frac { \ln | x | + C } { 2 } }$
D) $y = \sqrt { 2 \ln ^ { 2 } x + C }$
E) $y = \sqrt { \frac { \ln ^ { 2 } ( x + 2 ) } { C } }$