Home
Class 12
MATHS
If a curve y=f(x) passes through the poi...

If a curve `y=f(x)` passes through the point `(1,-1)` and satisfies the differential equation `,y(1+x y)dx""=x""dy` , then `f(-1/2)` is equal to: (1) `-2/5` (2) `-4/5` (3) `2/5` (4) `4/5`

A

`-4/5`

B

`2/5`

C

`4/5`

D

`-2/5`

Text Solution

Verified by Experts

The correct Answer is:
C
`y(1+xy)dx=xdy`
`rArr ydx-xdy+xy^(2)dx=0`
`rArr y^(2)d(x/y)+xy^(2)dx=0`
`rArr x/y+x^(2)/2=C`………….(1)
Curve passes through `(1,-1)`
`rArr -1+1/2=C` (form 1)
`rArr C=-1/2`
`rArr C=-1/2`
`rArr x/y+x^(2)/2=-1/2`
Now put `x=-1/2`
`rArr (-1/2)/(y)+(1/4)1/(2)=-1/2`
`rArr -1/(2y)=-1/2-1/8`
`y=4/5`
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 the curve y=f(x) passes through the point (1, -1) and satisfies the differential equation : y(1+xy)dx=x dy , then f(- 1/2) is equal to :

If a curve y=f(x) passes through the point (1,-1) and satisfies the differential equation ,y(1+xy)dx=xdy, then f(-(1)/(2)) is equal to: (A)-(2)/(5)(B)-(4)/(5)(C)(2)/(5)(D)(4)/(5)

If the curve y=f(x) passing through the point (1,2) and satisfies the differential equation xdy+(y+x^(3)y^(2))dx=0 ,then

If y=f(x) passing through (1,2) satisfies are differential equation y(1+xy)dx-x dy=0, then

Let a curve passes through (3, 2) and satisfied the differential equation (x-1) dx + 4(y -2) dy = 0

A curve passes through (1,0) and satisfies the differential equation (2x cos y+3x^(2)y)dx+(x^(3)-x^(2)sin y-y)dy=0

The equation of the curve passing through the point (1,1) and satisfying the differential equation (dy)/(dx) = (x+2y-3)/(y-2x+1) is