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The differential equation of all circles passing through the origin and having their centres on the x-axis is (1) `x^2=""y^2+""x y(dy)/(dx)` (2) `x^2=""y^2+"3"x y(dy)/(dx)` (3) `y^2=x^2""+"2"x y(dy)/(dx)` (4) `y^2=x^2""-"2"x y(dy)/(dx)`

A

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

B

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

C

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

D

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

Text Solution

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The correct Answer is:
D
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AAKASH INSTITUTE-DIFFERENTIAL EQUATIONS-Assignment Section - B (Objective Type Questions (One option is correct))
  1. The differential equation representing the family of curves y^2=2c(...

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  2. The differential equation of the family of curves y = P(x+Q)^(2) is

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  3. The differential equation of all circles passing through the origin...

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  4. The solution of (dy)/(dx) = (ax + h)/(by + k) represents a parabola wh...

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  5. The order of the differential equation of ellipse whose major and mino...

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  6. The differential equation of all parabolas whose axis are parallel ...

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  7. The solution of the equation 2xy' - y = 3 represents a family of

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  8. If (dp)/(dy) = 3^(cos y) sin y, then P is equal to

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  9. The solution of (dy)/(dx)-y=1, y(0)=1 is given by y(x)=

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  10. The general solution of the differential equaiton (1+y^(2))dx+(1+x^(2)...

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  11. The solution of the differential equation y(dy)/(dx)=x-1 satisfying y(...

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  12. Solution of the differential equation sin x. cos y dy + cos x. sin y d...

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  13. Solution of differential equation (dy)/(dx) = (2)/(x+y) is

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  14. The differential equation (dy)/(dx)=(sqrt(1-y^2))/y determines a fa...

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

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  16. The slope of tangent at (x,y) to a curve passing through (2, 1) is (x...

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  17. The solution of the differential equation (dy)/(dx) = (y)/(x)+ (Q((...

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  18. The solution of differential equation x^(2)y^(2)dy = (1-xy^(3))dx is

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

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  20. The solution of the differential equation ydx+ (x +x^2 y) dy =0 is

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