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If (2+sinx)(dy)/(dx)+(y+1)cosx=0 and y(0...

If `(2+sinx)(dy)/(dx)+(y+1)cosx=0` and `y(0)=1`, then `y((pi)/(2))` is equal to

A

`4/3`

B

`1/3`

C

`-2/3`

D

`-1/3`

Text Solution

Verified by Experts

The correct Answer is:
B
We have `(2+sinx)(dy)/(dx) +(y+1)cosx=0`
`rArr d/(dx)[(2sinx)(y+1)]=0`
`rArr (2+sinx)(y+1)=c`
Since `y(0)=1, c=4`
So, `y+1=4/(2+sinx)`
`therefore y(pi/2)=4/3-1=1/3`
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