Differentiation Question 451
Question: The differential equation satisfied by the function $ y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+…..\infty }}} $ , is
[MP PET 1998; Pb. CET 2001]
Options:
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)\cos x+\frac{dy}{dx}=0 $
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Answer:
Correct Answer: D
Solution:
$ y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+…..\infty }}} $
$ \Rightarrow y=\sqrt{\sin x+y}\Rightarrow y^{2}=\sin x+y $
On differentiating both sides, we get $ 2y\frac{dy}{dx}=\cos x+\frac{dy}{dx}\Rightarrow \frac{dy}{dx}(2y-1)=\cos x $ .
BETA
