Question

The integrating factor of the differential equation $\frac{dy}{dx}\left(x\log x\right)+y=2\log x$ is given by:

• A. $e^x$
• B. $\log x$
• C. $\log \left(\log x\right)$
• D. $x$

Answer 1

The correct option is B $\log x$

$\frac{dy}{dx}\left(x\log x\right)+y=2\log x$
$\Rightarrow \frac{dy}{dx}+\frac{y}{x\log x}=\frac{2}{x}$
Here, $P=\frac{1}{x\log x},Q=\frac{2}{x}$
$\therefore IF=e^{\int Pdx}=e^{\int \frac{dx}{x\log x}}$
$=\log x$