Find- d2ydx2 y - sin log x

Given y = sin (log x) →dydx = cos (log x) ·1x #160; #160; #160; [∵ assuming base to be e] →d^2ydx^2 = sin (log x) 1x^2 cos ...

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Byju's Answer

Standard XII

Mathematics

Logarithmic Differentiation

Find: d2ydx...

Question

Find: $\frac{d^{2} y}{d x^{2}}$
$y = sin (l o g x)$

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Solution

Given
$y = sin (log x)$
$\to \frac{d y}{d x} = cos (log x) \cdot \frac{1}{x}$ $[∵$ assuming base to be $e]$
$\to \frac{d^{2} y}{d x^{2}} = - sin (log x) \frac{1}{x^{2}} - cos (log x) \frac{1}{x^{2}}$

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Which of the following differential equations has $y = c_{1} e^{x} + c_{2} e^{- x}$ as the general solution?
(a) $\frac{d^{2} y}{d x^{2}} + y = 0$
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