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

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

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