The differential equation satisfied by the function y = x + x + x… - Vidyadip

MCQ

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

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

✓

Answer

Correct option: D.

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

d
(d) $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}} $

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

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