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. $\log \left(\log x\right)$
• D. $x$

Answer 1

The correct option is B $\log x$

Given differential equation can be rewritten as
$\frac{dy}{dx}+\frac{1}{x\log x}\cdot y=\frac{2}{x}$
$\therefore IF=e^{\int \frac{1}{x\log x}dx}=e^{\int \frac{1/x}{\log x}dx}=e^{\log \log x}=\log x$