Q. The integrating factor of the differential equation $\left( y\log y \right)dx = \left( \log y - x \right)dy\ is$
A) $\frac{1}{\log y}$
B) $\log{(\log y)}$
C) $1 + \log y$
D) $\log y$
Explanation
(d)
Given differential equation can be rewritten as
$\frac{dx}{dy} = \frac{(\log{y - x})}{y\log y}$
$\Rightarrow$ $\frac{dx}{dy} + \frac{x}{y\log y} = \frac{1}{y}$
$\therefore$ $IF = e^{\int_{}^{}{\frac{1}{y\log y}\ dy}}$
$= e^{\log{\log y}} = \log y$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.