Q. 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) $x$
Explanation
(b)
Given differential equation can be rewritten as
$\frac{dy}{dx} + \frac{1}{x\log x}.y = \frac{2}{x}$
$\therefore$ $IF = e^{\int_{}^{}{\frac{1}{x\log x}\ dx}} = e^{\int_{}^{}{\frac{\frac{1}{x}}{\log x}\ dx}} = e^{\log{\log x}} = \log x$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.