Question

The general solution of the differential equation $dy-\left(\sin x\sin y\right)dx=0,$ where $c$ is a constant of integration, is

• A. $e^{\cos x}\cdot \left|\tan \frac{y}{2}\right|=|c|$
• B. $e^{\cos x}\cdot |\tan y|=|c|$
• C. $\cos x\cdot |\tan y|=|c|$
• D. $\cos x\cdot |\sin y|=|c|$

Answer 1

The correct option is A $e^{\cos x}\cdot \left|\tan \frac{y}{2}\right|=|c|$

Given,
$dy-\left(\sin x\sin y\right)dx=0$
$\Rightarrow dy=\left(\sin x\sin y\right)dx$
$\Rightarrow \int \left(\text{cosec}y\right)dy=\int \sin xdx$
$\Rightarrow \ln \left|\tan \frac{y}{2}\right|=-\cos x+\ln |c|\Rightarrow \ln \left|\frac{\tan \frac{y}{2}}{c}\right|=-\cos x\Rightarrow \left|\frac{\tan \frac{y}{2}}{c}\right|=e^{-\cos x}\Rightarrow e^{\cos x}\cdot \left|\tan \frac{y}{2}\right|=|c|$