If y = sin (sin x), prove that $\frac{d^{2} y}{{dx}^{2}} + \tan x \frac{dy}{dx} + y \cos^{2} x = 0$

Solution

As y = sin (sin x)

$\Rightarrow \frac{dy}{dx} = \cos (\sin x) \cos x . . . . (i) and \frac{d^{2} y}{{dx}^{2}} = \cos (\sin x) (- \sin x) - \cos^{2} x (\sin (sinx)) Now \frac{d^{2} y}{{dx}^{2}} + \tan x \frac{dy}{dx} + y \cos^{2} x = - sinx \cos (\sin x) - \cos^{2} x \sin (\sin x) + \frac{\sin x}{\cos x} x \cos x \cos (\sin x) + \sin (\sin x) \cos^{2} x = - \sin x \cos (\sin x) - \cos^{2} x sion (\sin x) + \sin x \cos (\sin x) + \cos^{2} x \sin (\sin x) = 0 = R . H . S Hence we have proved that \frac{d^{2} y}{{dx}^{2}} + \tan x \frac{dy}{dxx} + y \cos^{2} x = 0 for y = \sin (\sin x)$

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Differential Equations

If y = sin (sin x), prove that $\frac{d^{2} y}{{dx}^{2}} + \tan x \frac{dy}{dx} + y \cos^{2} x = 0$

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Differential Equations

If y = sin (sin x), prove that d2 ydx2 + tan x dydx + y cos2 x = 0

Some More Questions From Differential Equations Chapter

Mock Test Series

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Entrance Exams Preparation

If y = sin (sin x), prove that $\frac{d^{2} y}{{dx}^{2}} + \tan x \frac{dy}{dx} + y \cos^{2} x = 0$