Question

The solution of the differential equation $cos \,x \,sin\, y\, dx + sin\, x\, cos \,y \,dy = 0$ is

• A. $\frac{sin\,x}{sin\,y}=c$
• B. $sin \,x \,sin\,y = c$
• C. $sin \,x + sin\, y =c$
• D. $cos\,x \,cos\,y =c$

Answer 1

Answer: (B)

$cosx\, siny\, dx + sinx \,cosy \,dy = 0$
$\frac{cos\,xdx}{sin\,x}=-\frac{cos\,ydx}{sin\,y}$
On integrating, we get
$log \,sinx = - log\, siny + logc$
$\Rightarrow log\,sinx+log\,siny=logc$
$\Rightarrow sinx\,siny=c$