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Find the equation of a curve passing thr...

Find the equation of a curve passing through `(2,7/2)` and having gradient `1-1/(x^2)` at `(x , y)` is

A

`y=x^(2)+x+1`

B

`xy=x^(2)+x+1`

C

`xy=x+1`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
We have `(dy)/(dx)=1-1/x^(2)` or `y=x+1/x+C`
This passes through `(2,7//2)`
Therefore, `7/2=2+1/2+C` or `C=1`
Thus, the equation of the curve is
`y=x+1/x+1` or `xy=x^(2)+x+1`
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CENGAGE-DIFFERENTIAL EQUATIONS-Exercise (Single)
  1. The solution of the differential equation x^2(dy)/(dx)cos(1/x)-ysin(1/...

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  2. The solution of (dy)/(dx)=(x^2+y^2+1)/(2x y) satisfying y(1)=1 is

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  3. The solution of the differential equation (dy)/(dx)=1/(x y[x^2siny^2+1...

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  4. Find the equation of a curve passing through (2,7/2) and having grad...

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  5. Which of the following is not the differential equation of family o...

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  6. Tangent to a curve intercepts the y-axis at a point Pdot A line ...

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  7. Orthogonal trajectories of family of the curve x^(2/3)+y^(2/3)=a^((2/3...

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  8. The curve in the first quadrant for which the normal at any point (...

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  9. The equation of the curve which is such that the portion of the axi...

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  10. The family of curves represented by (dy)/(dx)=(x^(2)+x+1)/(y^(2)+y+1) ...

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  11. A normal at P(x , y) on a curve meets the x-axis at Q and N is the ...

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  12. A curve is such that the mid-point of the portion of the tangent in...

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  13. The normal to a curve at P(x , y) meet the x-axis at Gdot If the ...

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  14. The x-intercept of the tangent to a curve is equal to the ordinate of ...

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  15. The equation of a curve passing through (1,0) for which the product...

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  16. The curve with the property that the projection of the ordinate on ...

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  17. Spherical rain drop evaporates at a rate proportional to its surfac...

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  18. Water is drained from a vertical cylindrical tank by opening a valv...

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  19. The population of a country increases at a rate proportional to the...

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  20. An object falling from rest in air is subject not only to the gravi...

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