Solve the differential equation.
-$$\frac { d y } { d x } = 7 x ^ { 6 } e ^ { - y }$$
A) $y = \ln \left( 7 x ^ { 7 } + C \right)$
B) $y = x ^ { 7 } + C$
C) $y = C \ln \left( x ^ { 7 } \right)$
D) $y = \ln \left( x ^ { 7 } + C \right)$

Question

Quizplus · Accepted Answer

We can separate variables and obtain 
$$\frac { d y } { e ^ { y } } = 7 x ^ { 6 } d x .$$
Integrating both sides gives 
$$-e ^ { - y } = x ^ { 7 } + C,$$
or equivalently, 
$$y = \ln \left( x ^ { 7 } + C \right).$$
Therefore, the correct answer is D.

Solve the Differential Equation dydx=7x6e−y\frac { d y } { d x } = 7 x ^ { 6 } e ^ { - y }dxdy​=7x6e−y

Solve the Differential Equation $\frac { d y } { d x } = 7 x ^ { 6 } e ^ { - y }$