Question

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

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

Answer 1

The correct option is C $logx$

The given differential equation can be rewritten as $\frac{dy}{dx}+\frac{1}{xlogx}y=\frac{2}{x}$ which is linear in y.
$\therefore IF=e^{\int \frac{1}{xlogx}dx}=e^{log\left(logx\right)}=logx$