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Form the differential equation from the following primitives where constants are arbitrary: `y^2=4a x`

Text Solution

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`y^2=4axldots`(1)
Differentiating it with respect to `x`, we get
`2y{dy}/{dx}=4aldots`(2)
From (1) and (2),
`a=1/2y{dy}/{dx}`
Putting value of `a` in (1), we get
`y^2=4 xx1/2y{dy}/{dx}x`
`implies 2x{dy}/{dx}=y`
...
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Knowledge Check

  • The differential equation for the family of curves x^2+y^2-2ay=0 , where a is an arbitrary constant is

    A
    `(x^2-y^2)y'=2xy`
    B
    `2(x^2+y^2)y'=xy`
    C
    `2(x^2-y^2)y'=xy`
    D
    `(x^2+y^2)y'=2xy`

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