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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

`1//3`

B

`2//3`

C

`-1//3`

D

1

Text Solution

Verified by Experts

The correct Answer is:
A
`1/(y+1)dy=-(cosx)/(2+sinx)dx`
Integrating, we get
`log(y+1)+logk+log(2+sinx)=0`
`therefore k(y+1)(2+sinx)=1` when `x=0, y=1` where k is constant.
`therefore 4k=1` or `k=1//4`
`therefore (y+1)(2+sinx)=4`
Now, put `x=pi/2`
`therefore (y+1)3=4 therefore y=1//3`
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CENGAGE-DIFFERENTIAL EQUATIONS-Exercise (Single)
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