The integrating factor of the differential equation $x \frac{d y}{d x}+y-x+x y \cot x=0$, (x ≠ 0) is:
Answer & explanation
Correct answer: option 1
$x \frac{dy}{dx}+y-x+x y \cot x=0$, (x ≠ 0)
$⇒\frac{dy}{dx}+(\frac{1}{x}+cotx)y=1$ ⇒ Integrating factor = $e^{\int(\frac{1}{x}+cotx)dx}$
$⇒e^{logx+log\, sinx}⇒x\, sinx$
So, option A is correct.