Solve the Initial-Value Problem $x y ^ { \prime } - y = x \ln x , \quad y ( 1 ) = 3$

Multiple Choice

Solve the initial-value problem.
$x y ^ { \prime } - y = x \ln x , \quad y ( 1 ) = 3$

A) $y ( x ) = 3 x ( \ln x ) ^ { 2 }$
B)
$y ( x ) = \frac { 1 } { 2 } x ( \ln x ) ^ { 2 } + 3 x$
C)
$y ( x ) = 3 x \ln x + \frac { 1 } { 2 } x$
D)
$y ( x ) = 3 \ln x + \frac { 1 } { 2 } x$
E)
$y ( x ) = \frac { 1 } { 2 } ( \ln x ) ^ { 3 } + x$