Q. The integrating factor of $x\ \frac{dy}{dx} + (1 + x)y = x$ is
A) $x$
B) $2x$
C) $e^{x\log x}$
D) $xe^{x}$
Explanation
(d)
$x\ \frac{dy}{dx} + (1 + x)y = x$
$\Rightarrow$ $\frac{dy}{dx} + \frac{1 + x}{x}y = 1$
$IF = e^{\int_{}^{}{\frac{1 + x}{x}\ dx}}$
$= e^{\int_{}^{}\frac{dx}{x} + \int_{}^{}{dx}}$
$= e^{\log x + x}$
$= xe^{x}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.