Solve the differential equation.
-$$\frac { d y } { d x } = 4 \cos x \sec y$$
A) $y = 4 \sin x + C$
B) $y = \sin ^ { - 1 } ( 4 \sin x + C )$
C) $y = \sin ^ { - 1 } ( 4 \cos x + C )$
D) $y = \sin ( 4 \sin x + C )$

Question

Quizplus · Accepted Answer

We can start by separating variables and integrating both sides:

$$\int \sec y dy = \int 4\cos x dx$$

Using the substitution $u = \sin y$, $du = \cos y dy$, we get:

$$\ln|\sec y + \tan y| = 4\sin x + C$$

Taking the inverse sine of both sides:

$$y = \sin ^ { - 1 } ( \sec y + \tan y ) = \sin ^ { - 1 } ( 4 \sin x + C )$$

So the answer is B.

Solve the Differential Equation dydx=4cos⁡xsec⁡y\frac { d y } { d x } = 4 \cos x \sec ydxdy​=4cosxsecy

Solve the Differential Equation $\frac { d y } { d x } = 4 \cos x \sec y$