Q. An integrating factor of the differential equation $\left( 1 + y + x^{2}y \right)dx + \left( x + x^{3} \right)dy = 0$ is
A) $\log x$
B) $x$
C) $e^{x}$
D) $\frac{1}{x}$
Explanation
(b)
Given, $\frac{dy}{dx} = - \frac{1 + y + x^{2}y}{x + x^{3}}$
$\Rightarrow$ $\frac{dy}{dx} + \frac{y}{x} = - \frac{1}{x(1 + x^{2})}$
$\therefore$ $IF = e^{\int_{}^{}{\frac{1}{x}\ dx}} = x$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.