Solve the Differential Equation $4 \frac { d w } { d t } + 5 e ^ { t + w } = 0$

Multiple Choice

Solve the differential equation.
$4 \frac { d w } { d t } + 5 e ^ { t + w } = 0$

A) $w = \frac { 5 } { 4 } e ^ { t } - C$
B) $w = \ln \left( \frac { 4 } { 5 } t \right) - t$
C)
$w = - \ln \left( \frac { 5 e ^ { t } } { 4 } - C \right)$
D)
$w = \ln \left( \frac { 4 } { 5 } + \frac { 4 } { 5 } C e ^ { t } \right) - t$
E) none of these