A) 1/3
B) 2/3
C) -1/3
D) 1
Correct Answer: A
Solution :
[a] \[\frac{dy}{dx}\left( \frac{2+\sin x}{1+y} \right)=-\cos x,y(0)=1\] \[\Rightarrow \frac{dy}{(1+y)}=\frac{-\cos x}{2+\sin x}dx\] Integrating both sides \[\Rightarrow \,\,\,ln(1+y)=-ln(2+sin\,x)+C\] Put x = 0 and y = 1 \[\Rightarrow \,\,\,ln(2)=-ln2+C\Rightarrow C=\,\,ln\,\,4\] Put \[x=\frac{\pi }{2}\] \[ln\,(1+y)=-ln3+ln4=ln\frac{4}{3}\Rightarrow y=\frac{1}{3}\]You need to login to perform this action.
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