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if y=y(x) and (2+sinx)/(y+1)((dy)/(dx))=...

if `y=y(x)` and `(2+sinx)/(y+1)((dy)/(dx))=-cosx ,y(0)=1,` then `y(pi/2)=` (a) `( b ) (c) (d)1/( e )3( f ) (g) (h)` (i) (b) `( j ) (k) (l)2/( m )3( n ) (o) (p)` (q) (c) `( r ) (s)-( t )1/( u )3( v ) (w) (x)` (y) (d) 1

A

(a) 1/3

B

(b) 2/3

C

(c) -1/3

D

(d) 1

Text Solution

Verified by Experts

The correct Answer is:
(a)
Given, `dy/dx=(-cosx(y+1))/(2+sin x)`
`rArr dy/(y+1)=(-cosx)/(2+sinx)dx`
On integrating both sides
`int dy/(y+1)=-int (cosx)/(2+sinx)dx`
`rArr log (y+1)=-log(2+sin x) +log e`
When `x =0, y=1 rArr c = 4`
`rArr y+1=4/(2+sin x`
`therefore y(pi/2)=4/3-1`
`rArr y(pi/2)=1/3`
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