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The differential equation of all circles...

The differential equation of all circles passing through the origin and having their centres on the X-axis is

A

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

B

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

C

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

D

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

Text Solution

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The correct Answer is:
C
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AAKASH SERIES-DIFFERENTIAL EQUATIONS-Exercise - II
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  2. The differential equation by eliminating a, b from (x-a)^(2) + (y-b)^(...

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

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  4. The differential equation of the family of circles of fixed radius r a...

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  5. The differential equation of the family of parabolas with focus at ori...

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  6. The differential equation of the system of curves given by (x^(2))/(a^...

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  7. The solution of (xdx + ydx)/(x^(2) + y^(2)) = 0 is

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

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  9. Tan^(-1)(x) + Tan^(-1)(y) = c is the solution of

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  10. The solution of xd(xy) = ((f(xy))/(f^(1)(xy)))dx is

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  11. The solution of (e^(x) + 1) y dy + (y+ 1) dx = 0 is

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  12. If 2f(x) = f'(x) and f(0) = 3 then f(2) =

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  13. The solution of (dy)/(dx) = (x log x^(2) + x)/(sin y + y cos y) is

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  14. The solution of y-x((dy)/(dx)) = a(y^(2) + (dy)/(dx)) is

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

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  16. The solution of x dx + ydx = x^(2)y dy - xy^(2)dx is

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  17. The solution of y dx - xdy + 3x^(2) y^(2) e^(x^(3))dx = 0 is

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  18. The solution of (dy)/(dx) = 2xy - 3y + 2x - 3 is

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  19. The solution of log((dy)/(dx)) = ax + by is

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  20. The solution of y^(2) cos sqrt(x) dx-sqrt(x e)^((1)/(y)) dy = 0 is

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