Question

The solution of the differential equation $\left(\frac{dy}{dx}\right)\tan y=\sin (x+y)+\sin (x-y)$ is

• A. $secx-1/2tany=c$
• B. $logsin\text{ (}x+y)=c$
• C. $secx+tany=c$
• D. $secy+2cosx=c$

Answer 1

Answer: (D)

Given, differential equation is
$\left(\frac{dy}{dx}\right)\tan y=\sin (x+y)+\sin (x-y)$
$\Rightarrow$ $\left(\frac{dy}{dx}\right)\tan y=2\sin x\cos y$
$\Rightarrow$ $\frac{\sin y}{{\cos }^{2}y}dy=2\sin xdx$
On integrating both sides, we get $\frac{1}{\cos y}=-2\cos x+c$
$\Rightarrow$ $\sec y+2\cos x=c$