JEE Main Solved Paper 2017 Question 16
Question: If $ (2+\sin x)\frac{dy}{dx}+(y+1)\cos x=0 $ and $ y(0)=1, $ then $ y( \frac{\pi }{2} ) $ is equal to:- [JEE Main Solved Paper-2017]
Options:
A) $ \frac{4}{3} $
B) $ \frac{1}{3} $
C) $ -\frac{2}{3} $
D) $ -\frac{1}{3} $
Show Answer
Answer:
Correct Answer: B
Solution:
$ (2+\sin x)\frac{dy}{dx}+(y+1)\cos x=0 $
$ \frac{d}{dx}(2+\sin x)(y+1)=0 $
$ x=0,y=1\Rightarrow c=4 $
$ y+1=\frac{4}{2+\sin x} $
$ y( \frac{\pi }{2} )=\frac{4}{3}-1=\frac{1}{3} $
