Question

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

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

Answer 1

Answer: (B)

Given differential equation can be rewritten as

$\frac{dy}{dx}+\frac{1}{xlogx}\cdot y=\frac{2}{x}$

$\therefore$ IF $=e^{\int \frac{1}{xlogx}dx}$

$=e^{\int \frac{1/x}{logx}dx}$

$=e^{loglogx}$

$=logx$