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COMEDK · Maths · 32. Differential Equations

The solution of the differential equation \(x \dfrac{d y}{d x}=\cot y\) is

  1. A \(y \cos x=c\)
  2. B \(x \cos y=c\)
  3. C \(\log (x \cos y)=c\)
  4. D \(\log (y \cos x)=c\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(x \cos y=c\)

Step-by-step Solution

Detailed explanation

The given differential equation is \(x \dfrac{dy}{dx} = \cot y\). Separating the variables, we get \(\dfrac{dy}{\cot y} = \dfrac{dx}{x}\). This simplifies to \(\tan y \, dy = \dfrac{dx}{x}\). Integrating both sides, we have \(\int \tan y \, dy = \int \dfrac{dx}{x}\). The…