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If the differential equation representing the family of all circles touching x-axis at the origin is `(x^2-y^2)(dy)/(dx)=g(x)y`, then g(x) equals

A

`1/2x`

B

`2x^2`

C

2x

D

`1/2x^2`

Text Solution

Verified by Experts

The correct Answer is:
C
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Knowledge Check

  • The differential equation representing a family of circles touching Y-axis at the origin, is

    A
    `x^(2) +y^(2) - 2xy (dy)/(dx) = 0`
    B
    `x^(2) + y^(2) + 2xy (dy)/(dx) = 0`
    C
    `x^(2) - y^(2) - 2xy (dy)/(dx) = 0`
    D
    `x^(2) - y^(2) + 2 xy (dy)/(dx) = 0`

  • If the differential equation representing the family of all touching y-axis at the origin is x^2-y^2=f(x)y(dx)/(dy) the nf(x) is equal to

    A
    2x
    B
    x
    C
    `x^2`
    D
    3x

  • The differential equation y(dy)/(dx)+x=C represents

    A
    family of hyperbolas
    B
    family of parabolas
    C
    family of ellipses
    D
    family of circles

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