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Question

(C) Given the differential equation: $\frac{dy}{dx} + \sin^2 y = 0$. Rearranging the terms to separate the variables,we get: $\frac{dy}{dx} = -\sin^2

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$x = \cot y + c$

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(C) Given the differential equation: $\frac{dy}{dx} + \sin^2 y = 0$. Rearranging the terms to separate the variables,we get: $\frac{dy}{dx} = -\sin^2 y$. Dividing both sides by $\sin^2 y$ and multiplying by $dx$,we obtain: $\frac{dy}{\sin^2 y} = -dx$. This can be written as: $\csc^2 y \, dy = -dx$. Integrating both sides: $\int \csc^2 y \, dy = \int -dx$. Since $\int \csc^2 y \, dy = -\cot y$,we have: $-\cot y = -x + C$. Multiplying by $-1$,we get: $\cot y = x - C$. Letting $-C = c$,we obtain: $x = \cot y + c$.

The solution of the differential equation $\frac{dy}{dx} + \sin^2 y = 0$ is

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