Question

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

• A. $e^{x}$
• B. $log\, x$
• C. $log \, (log\, x)$
• D. $x$

Answer 1

Answer: (B)

Given differential equation can be rewritten as

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

$\therefore $ IF $=e^{\int\frac{1}{x\,log\,x}dx}$

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

$=e^{log\,log\,x}$

$=log\,x$