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The differential equation of the family of curves of `x^(2)+y^(2)-2ay=0` where a is arbitary constant, is

A

`(x^(2)-y^(2))(dy)/(dx)=2xy`

B

`2(x^(2)+y^(2))(dy)/(dx)=xy`

C

`2(x^(2)-y^(2))(dy)/(dx)=xy`

D

`(x^(2)-y^(2))(dy)/(dx)=2xy`

Text Solution

Verified by Experts

Given equation of curve is `x^(2)+y^(2)-2ay=0`
`Rightarrow (x^(2)+y^(2))/(y)=2a`
On differentiation both sides, w.r.t. we get
`(y(2x+2y(dy)/(dx))-(x^(2)+y^(2))(dy)/(dx))/(y^(2))=0`
`Rightarrow 2xy+2y^(2)(dy)/(dx)-(x^(2)+y^(2))(dy)/(dx)=0`
`Rightarrow (2y^(2)-x^(2)-y^(2))(dy)/(dx)=-2xy`
`Rightarrow (y^(2)-x^(2))(dy)/(dx)=-2xy`
`Rightarrow (x^(2)-y^(2))(dy)/(dx)=2xy`
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NCERT EXEMPLAR-DIFFERENTIAL EQUATIONS -Differential Equations
  1. The solution the differential equation "cos x sin y dx" + "sin x c...

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

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  3. The differential equation of the family of curves of x^(2)+y^(2)-2ay=0...

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  4. The family y=Ax+A^(3) of curves is represents by differential equation...

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  5. The general solution of (dy)/(dx)=2xe^(x^(2)-y) is

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  6. The curve for which the slope of the tangent at any point is equal to ...

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  7. The general solution of differential equation (dy)/(dx)=e^((x^(2))/(2)...

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  8. The solution of equation (2y-1)dx-(2x+3)dy=0 is

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  9. The differential equation for which y=a cos x+b sin x is a solution is

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  10. The solution of (dy)/(dx)+y=e^(-x), y(0)=0 "is"

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  11. The order and degree of differential equation: ((d^(3)y)/(dx^(3)))^(...

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  12. The order and degree of differential equation: [1+((dy)/(dx))^(2)]=(d^...

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  13. The differential equation of family of curves of y^(2)=4a(x+a)is

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  14. Which of the following is a general solution of (d^(2)y)/(dx^(2))-2(dy...

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  15. The general solution of (dy)/(dx)+y tan x=sec x is

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  16. The solution of differential equation (dy)/(dx)+(y)/(x)=sin x is

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  17. The general solution of differential equation (dy)/(dx)=e^((x^(2))/(2)...

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  18. The solution of differential equation (dy)/(dx)=e^(x-y)+x^(2)e^(-y)is

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  19. The solution of differential equation (dy)/(dx)+(2xy)/(1+x^(2))=(1)/(1...

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  20. (i) The degree of the differential equation (d^(2)y)/(dx^(2))+e^(dy//d...

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