Question

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

• A. $(2y-1)\frac{dy}{dx}-\sin x=0$
• B. $(2y-1)\cos x+\frac{dy}{dx}=0$
• C. $(2y-1)\cos x-\frac{dy}{dx}=0$
• D. $(2y-1)\frac{dy}{dx}-\cos x=0$

Answer 1

Answer: (D)

$y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+.....\infty }}}$
$\Rightarrow y=\sqrt{sinx+y}\Rightarrow y^2=\sin x+y$
On differentiating both sides, we get
$2y\frac{dy}{dx}=\cos x+\frac{dt}{dx}\Rightarrow \frac{dy}{dx}\left(2y-1\right)=\cos x$