The general solution of the differential equation d y d x = cot x cot y is:

Question

The general solution of the differential equation $\frac{d y}{d x} = \cot x \cot y$ is:

Smart Achievers · Accepted Answer

(2)

Ans. $\sin x = C \sec y$

Explanation:

$\frac{d y}{d x} = \cot x \cot y$

$\Rightarrow$ $\cot x d x - \tan y d y = 0$

Integrating on both sides, we get

$\Rightarrow$ $\int \cot x d x - \int \tan y d y = 0$

$\log \sin x - \log \sec y = \log C$

$\Rightarrow$ $\log (\frac{\sin x}{\sec y}) = \log C$

$\Rightarrow$ $\sin x = C \sec y$

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