A) 1
B) \[\frac{1}{2}\]
C) \[\frac{1}{3}\]
D) \[\frac{1}{4}\]
Correct Answer: C
Solution :
The given differential equation is \[\frac{\cos x}{2+\sin x}\,dx+\frac{dy}{y+1}=0\] Þ \[\log (2+\sin x)+\log (y+1)=\log c\] Þ \[(y+1)\,(2+\sin x)=c\] Þ \[2\times 2=c\] Þ \[c=4\] Thus, \[y+1=\frac{4}{2+\sin x}\]Þ\[y=\frac{2-\sin x}{2+\sin x}\] Þ \[y\,\left( \frac{\pi }{2} \right)=\frac{1}{3}\].You need to login to perform this action.
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