The integrating factor of the differential equation `"dy"/"dx" (x log x) + y` = 2logx is ______.

The integrating factor of the differential equation dydxdydx(xlogx)+y = 2logx is ______. - Mathematics

Question

The integrating factor of the differential equation $\frac{dy}{dx} (x \log x) + y$ = 2logx is ______.

Options

e^x
log x
log (log x)
x

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Solution

The integrating factor of the differential equation $\frac{dy}{dx} (x \log x) + y$ = 2logx is log x.

Explanation:

Given equation can be written as $\frac{dy}{dx} + \frac{y}{x \log x} = \frac{2}{x}$ .

Therefore, I.F. = $e^{\int \frac{1}{x \log x} d x}$

= $e^{\log (\log x)}$

= log x.

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Differential Equations

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Q 17 Q 16 Q 18

Chapter 9: Differential Equations - Solved Examples [Page 188]

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NCERT Exemplar Mathematics [English] Class 12

Chapter 9 Differential Equations
Solved Examples | Q 17 | Page 188

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The integrating factor of the differential equation dydxdydx(xlogx)+y = 2logx is ______. - Mathematics

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