The integrating factor of the differenti

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Differential Equations

Question:

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

Options:

x sin x

x cos x

sin x

Correct Answer:

x sin x

Explanation:

$x \frac{dy}{dx}+y-x+x y \cot x=0$, (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.