Question:
The integrating factor of the differential equation
\[
\sin x \frac{dy}{dx} + 2y \cos x = 1
\]
is:
The integrating factor of the differential equation
\[ \sin x \frac{dy}{dx} + 2y \cos x = 1 \]
is:
\[ \sin x \frac{dy}{dx} + 2y \cos x = 1 \]
is:
Show Hint
Always reduce to standard linear form before finding IF.
Updated On: Mar 23, 2026
- \(\sin^2 x\)
- \(\dfrac{2}{\sin x}\)
- \(\log|\sin x|\)
- (1)/(sin² x)
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The Correct Option is A
Solution and Explanation
Step 1: Write in linear form:
\[ \frac{dy}{dx} + 2y \cot x = \csc x \]
Step 2: Integrating factor:
\[ \text{IF} = e^{\int 2 \cot x \, dx} = e^{2 \ln \sin x} = \sin^2 x \]
\[ \frac{dy}{dx} + 2y \cot x = \csc x \]
Step 2: Integrating factor:
\[ \text{IF} = e^{\int 2 \cot x \, dx} = e^{2 \ln \sin x} = \sin^2 x \]
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