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(D) Given the function $y = \sqrt{\sin x + \sqrt{\sin x + \sqrt{\sin x + \dots \infty}}}$.Since the series is infinite,we can write it as $y = \sqrt{\

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$(2y - 1)\frac{dy}{dx} - \cos x = 0$

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(D) Given the function $y = \sqrt{\sin x + \sqrt{\sin x + \sqrt{\sin x + \dots \infty}}}$.Since the series is infinite,we can write it as $y = \sqrt{\sin x + y}$.Squaring both sides,we get $y^2 = \sin x + y$.Differentiating both sides with respect to $x$,we get $\frac{d}{dx}(y^2) = \frac{d}{dx}(\sin x + y)$.Using the chain rule,$2y \frac{dy}{dx} = \cos x + \frac{dy}{dx}$.Rearranging the terms,we get $2y \frac{dy}{dx} - \frac{dy}{dx} = \cos x$.Factoring out $\frac{dy}{dx}$,we get $(2y - 1)\frac{dy}{dx} = \cos x$,which can be written as $(2y - 1)\frac{dy}{dx} - \cos x = 0$.

The differential equation satisfied by the function $y = \sqrt{\sin x + \sqrt{\sin x + \sqrt{\sin x + \dots \infty}}}$ is

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