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The integrating factor of the differential equation $x \frac{d y}{d x}+y-x+x y \cot x=0$, (x ≠ 0) is: |
x sin x x cos x x sin x |
x sin x |
$x \frac{dy}{dx}+y-x+x y \cot x=0$, (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. |
