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

Multiple Choice

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

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) $y ( x ) = \frac { 1 } { 2 } ( \ln x ) ^ { 3 } + x$