Question

The general solution of the differential equation $\frac{dy}{dx}=cotxcoty$ is

• A. $\cos x=c\cos ecy$
• B. $\sin x=csecy$
• C. $\sin x=c\cos y$
• D. $\cos x=c\sin y$

Answer 1

The correct option is B

$\sin x=csecy$

Find the general solution of the differential equation

Given, $\frac{dy}{dx}=cotxcoty$

$$\begin{gathered} \Rightarrow \frac{dy}{coty}=cotxdx \\ \Rightarrow \int \tan ydy=\int cotxdx \\ \Rightarrow \log secy=\log \sin x+\log c\left[\because \int \tan \left(x\right)dx=\log \left(sec\left(x\right)\right)+c\right]\left[\because \int cotxdx=\log \left(\sin \left(x\right)\right)+c\right] \\ \Rightarrow secy=c\sin x \\ \Rightarrow csecy=\sin x \\ \Rightarrow \sin x=csecy \end{gathered}$$

Hence, option (B) is the correct answer.