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5. continuity and differentiation — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
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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