Solve the Initial-Value Problem $x y ^ { \prime } - y = x \ln x , \quad y ( 1 ) = 4$

Solve the initial-value problem. $x y ^ { \prime } - y = x \ln x , \quad y ( 1 ) = 4$

A) $y ( x ) = \frac { 1 } { 2 } ( \ln x ) ^ { 4 } + x$
B) $y ( x ) = 4 x \ln x + \frac { 1 } { 2 } x$
C) $y ( x ) = 4 \ln x + \frac { 1 } { 2 } x$
D) $y ( x ) = \frac { 1 } { 2 } x ( \ln x ) ^ { 2 } + 4 x$
E) $y ( x ) = 4 x ( \ln x ) ^ { 2 }$

Correct Answer:

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