Form the differential equation of the family of parabolas having a vertex at the origin and axis along positive y-axis.
Equation of the family of parabolas having a vertex at the origin and axis along positive y-axis can be represented by
(x)2 = 4ay, where a is an arbitrary constants.
Differentiating the above equation with respect to x on both sides, we have,
Substituting the value of a in equation (1)
This is the required differential equation.
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