Question

The integrating factor of \[ \frac{dy}{dx} + y \cot x = 2x + x^2 \cot x \] is

• A. \( \sin x \)
• B. \( \cos x \)
• C. \( \cot x \)
• D. \( \tan x \)

Hint:

Always convert to standard linear form before finding the integrating factor using \( e^{\int P(x) dx} \).

Answer 1

The Correct Option is A

Standard form of linear differential equation: \[ \frac{dy}{dx} + P(x) y = Q(x) \] Integrating factor (I.F.) is: \[ I.F. = e^{\int P(x) dx} \] Here, \( P(x) = \cot x \) So, \[ I.F. = e^{\int \cot x \, dx} = e^{\ln |\sin x|} = \sin x \]