Okay, faith. This is a separable differential equation. Step 1: Separate the variables. Multiply both sides by cos y and dx to get all y terms on one side and all x terms on the other. cos y dy = sin x dx Step 2: Integrate both sides. Integrate the left side with respect to y and the right side with respect to x. ∫ cos y dy = ∫ sin x dx Step 3: Perform the integration. The integral of cos y is sin y. The integral of sin x is −cos x. Remember to add the constant of integration, C. sin y = −cos x + C The general solution to the differential equation is: sin y = −cos x + C

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dy/dx = sin x / cosy

June 19, 2026Mathematics

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Answer

\sin y = -\cos x + C

Step-by-step solution

3 steps

Okay, faith. This is a separable differential equation.

Separate the variables.
Multiply both sides by $\cos y$ and $dx$ to get all $y$ terms on one side and all $x$ terms on the other.
$\cos y \, dy = \sin x \, dx$
Integrate both sides.
Integrate the left side with respect to $y$ and the right side with respect to $x$ .
$\int \cos y \, dy = \int \sin x \, dx$
Perform the integration.
The integral of $\cos y$ is $\sin y$ . The integral of $\sin x$ is $-\cos x$ . Remember to add the constant of integration, $C$ .
$\sin y = -\cos x + C$