Q52 / 150 · MHT CET 2020 (20 Oct Shift 2) · Mathematics

The integrating factor of the differential equation $\frac{d y}{d x}(x \log x)+y=4 \log x$ is

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

Solution

We have $\frac{d y}{d x}(x \log x)+y \quad=4 \log x$ $\therefore \frac{d y}{d x}+\left(\frac{1}{x \log x}\right) y=\frac{4}{x}$ $\therefore$ I.F. $=e^{\int \frac{d x}{x \log x}}=e^{\log (\log x)}=\log x$

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

Relevant Questions