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Form the differential equation of the family of parabolas having vertex at origin and axis along positive y-axis.

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We know the equation of the family of parabolas having vertex at the origin and axis along positive y-axis is
`x^2=4ay`
Differentiating w.r.t. x, we get,
`=>2x=(4ady)/(dx)`
​ `=>a=(xdx)/(2ady)`
Substituting the value of a,
`=>x^2=4×(xdx)/(2ady)×y`
`=>(xdy)/(dx)​=2y`
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