Q140 / 200 · Manipal (MET) 2011 · Mathematics

The solution of differential equation $d y-\sin x \sin y d x=0$ is

  • Correct answer
    A
    $e^{\cos x} \cdot \tan \frac{y}{2}=C$
  • B
    $e^{\cos x} \cdot \tan y=C$
  • C
    $\cos x \cdot \tan y=C$
  • D
    $\cos x \cdot \sin y=C$

Solution

Given equation can be rewritten as $\operatorname{cosec} y d y=\sin x d x$ On integrating both sides, we get $\begin{aligned} & \log \tan \frac{y}{2}=-\cos x+\log C \\ \Rightarrow \quad & \log \frac{\tan \frac{y}{2}}{C}=-\cos x \\ \Rightarrow \quad & \frac{\tan \frac{y}{2}}{C}=e^{-\cos x} \\ \Rightarrow \quad & e^{\cos x} \cdot \tan \frac{y}{2}=C\end{aligned}$

Hence, the correct answer is option: 'A'.

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