Q92 / 150 · MHT CET 2020 (20 Oct Shift 1) · Mathematics

The integrating factor of the differential equation y $\log _{y}\left(\frac{\mathrm{d} x}{\mathrm{dy}}\right)+x-\log \mathrm{y}=0$ is

  • A
    $\log (\log y)$
  • Correct answer
    B
    $\log y$
  • C
    $y$
  • D
    $e^{y}$

Solution

We have $y \log y\left(\frac{d x}{d y}\right)+x=\log y$ $\therefore \frac{\mathrm{dx}}{\mathrm{dy}}+\frac{\mathrm{x}}{\mathrm{y} \log \mathrm{y}}=\frac{1}{\mathrm{y}}$ $\therefore$ I.F. $=e^{\int \frac{1}{y \log y} d y}=e^{\log (\log y)}=\log y$

Hence, the correct answer is option: 'B'.

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