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

`-3/8`

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

Let y=g(x) be the solution of the differential equation sinx((dy)/(dx))+y cos x=4x, If y(pi/2)=0 , then y(pi/6) is equal to

If (dy)/(dx)=y+3 and y(0)=2 , then y(ln 2) is equal to

if y=y(x) and (2+sinx)/(y+1)((dy)/(dx))=-cosx ,y(0)=1, then y(pi/2)=

If y = y(x) is the solution of the differential equation, x dy/dx+2y=x^2 satisfying y(1) = 1, then y(1/2) is equal to

Solve : (dy)/(dx)+y=cosx

If y=sqrt(sinx+y),then (dy)/(dx)dot

Find (dy)/(dx) for y=sin^(-1)(cosx), where x in (0,2pi)dot

(1+x+xy^(2))(dy)/(dx)+(y+y^(3))=0

If ln((e-1)e^(xy) +x^2)=x^2+y^2 then ((dy)/(dx))_(1,0) is equal to

If x(dy)/(dx)=x^(2)+y-2, y(1)=1 , then y(2) equals ………………..