Question

The integrating factor of the differential equation $(y\log y)dx=(\log y-x)dy$ is

• A. $\frac{1}{\log y}$
• B. $\log (\log y)$
• C. $1+\log y$
• D. $\frac{1}{\log (\log y)}$
• E. $\log y$

Answer 1

Answer: (E)

Given differential equation can be rewritten as $\frac{dx}{dy}=\frac{(\log y-x)}{y\log y}$
$\Rightarrow$ $\frac{dx}{dy}+\frac{x}{y\log y}=\frac{1}{y}$
$\therefore$ $IF=e^{\int \frac{1}{y\log y}dy}$
$=e^{\log \log y}=\log y$