The integrating factor of the differential equation $\frac{dy}{dx} (x \log x) + y = 2 \log x$ is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $\log x$ ##
The given differential equation is
$\frac{dy}{dx} (x \log x) + y = 2 \log x$
Rewrite the differential equation:
$\frac{dy}{dx} + \frac{y}{x \log x} = \frac{2}{x}$
The integrating factor is
$e^{\int \frac{dx}{x \log x}} = e^{\log(\log x)} = \log x$