Question

Solution of differential equation $dy-sin\,x\,sin\,y dx=0$ is

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

Answer 1

Answer: (A)

$dy-sin\,x\,sin\,y\,dx=0$
or $dy=sin\,x\,sin\,y\,dx$
or $\int cosec\, y\,dy = \int\,sin\,xdx$
or $log\,tan \frac{y}{2}=-cos\,x+log\,c$
or $log \frac{tan \frac{y}{2}}{c}=-cos\,x$
or $\frac{tan \frac{y}{2}}{c}=e^{-cos\,x}$
or $e^{cos\,x} tan \frac{y}{2}=c$