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CONTINUITY AND DIFFERENTIABILITY — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSCONTINUITY AND DIFFERENTIABILITY5 Marks
Question
$\text{If y} = \sin (\log x) , \text{prove that}$$x^{2} \frac{d^{2}y}{dx^{2}} + x \frac{dy}{dx} + y =0$
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Answer

$y = \sin(\log x)$$\therefore \frac{dy}{dx} = \cos (\log x) . \frac{1}{x} \Rightarrow x \frac{dy}{dx} = \cos (\log x)$
$\therefore x \frac{d^{2}y}{dx^{2}} + \frac{dy}{dx} = \frac{-1}{x} \sin (\log x) = -\frac{y}{x}$
$\Rightarrow x^{2} \frac{d^{2}y}{dx^{2}} + x \frac{dy}{dx} + y = 0$

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