Solve the Differential Equation $\frac { d u } { d t } = 15 + 5 u + 3 t + u t$

Solve the differential equation. $\frac { d u } { d t } = 15 + 5 u + 3 t + u t$

A) $u = - 3 + C e ^ { \frac { t ^ { 2 } } { 2 } - 5 t }$
B) $u = - 3 + C e ^ { t ^ { 2 } - 5 t }$
C) $u = - 3 + C e ^ { \frac { t ^ { 2 } } { 2 } + 5 t }$
D) $u = - 3 + C e ^ { \frac { t ^ { 2 } } { 2 } + 5 t ^ { 2 } }$
E) $u = - 3 + C e ^ { t ^ { 2 } + 5 t }$

Correct Answer:

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