Differential Equations
Linear Differential Equations
Premium Question
Grade 12

Question:

The general solution of $\frac{dy}{dx} + y \cot x = \csc x$ is:
(1) $y \sin x = x + C$
(2) $y \cos x = x + C$
(3) $y = x \sin x + C$
(4) $y \sin x = -x + C$

Step-by-Step Solution

Key Concept: This is linear in $y$ with integrating factor $e^{\int \cot x \, dx} = \sin x$; multiply through by $\sin x$ and recognise the left side as $\frac{d}{dx}(y \sin x)$.
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Correct Answer: (1)

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