Solve the Differential Equation $( 6 + t ) \frac { d u } { d t } + u = 6 + t , t > 0$

Multiple Choice

Solve the differential equation. $( 6 + t ) \frac { d u } { d t } + u = 6 + t , t > 0$

A) $u = \frac { t ^ { 2 } + C } { t + 6 }$
B) $u = 6 t + \frac { t ^ { 2 } } { 6 } + C$
C) $u = \frac { 6 t + t ^ { 2 } + C } { t + 6 }$
D) $u = \frac { 6 t + \frac { t ^ { 2 } } { 2 } + C } { t + 6 }$
E)
$u = \frac { 6 t + \frac { 1 } { 2 } t ^ { 2 } } { \frac { 3 } { 6 } t + 2 } + C$