Home
Class 12
MATHS
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`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise JEE Advanced Previous Year|12 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Single Correct Answer Type|37 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Exercise (Numerical)|15 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise|337 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Numerical Value Type|3 Videos

Similar Questions

Explore conceptually related problems

If (2+sin x)(dy)/(dx)+(y+1)cos x=0 and y(0)=1, then y((pi)/(2)) is equal to

If (2+sin x)(dy)/(dx)+(y+1)cos x=0 and y(0)=1, then y((pi)/(2)) is equal to -(1)/(3)(2)(4)/(3) (3) (1)/(3)(4)-(2)/(3)

If (2+sin x)(dy)/(dx)+(y+1)cos x=0 and y(0)=1, then y((pi)/(2)) is equal to :

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

If ((2+cosx)/(3+y))(dy)/(dx)+sinx=0 and y(0)=1 , then y((pi)/(3)) is equal to

If y=y(x) and (2+sin x)/(y+1)((dy)/(dx))=-cos x,y(0)=1, then y((pi)/(2)) equals