Question

The general solution of the differential equation $\frac{dy}{dx}+\cos \frac{x+y}{2}=\cos \frac{x-y}{2}$ is :

• A. $\ln \left(\tan \frac{y}{4}\right)=C-2\cos \frac{x}{2}$
• B. $\ln \left(\tan \frac{y}{4}\right)=2\cos \frac{x}{2}-C$
• C. $\ln \left(\mathrm{cosec}\frac{y}{2}-\cot \frac{y}{2}\right)=C-2\cos \frac{x}{2}$
• D. $\ln \left(\mathrm{cosec}\frac{y}{2}+\cos \frac{y}{2}\right)=2\cos \frac{x}{2}-C$

Answer 1

Answer: (A), (C), (D)

Correct answer is (a) $\ln \left(\tan \frac{y}{4}\right)=C-2\cos \frac{x}{2}$ Correct answer is (c) $\ln \left(\mathrm{cosec}\frac{y}{2}-\cot \frac{y}{2}\right)=C-2\cos \frac{x}{2}$ Correct answer is (d) $\ln \left(\mathrm{cosec}\frac{y}{2}+\cos \frac{y}{2}\right)=2\cos \frac{x}{2}-C$