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

When the vertices of parabola at origin and axis along positive y - axis

Then, Equation of parabola is

x²=4ay …(i)

Now, Differentiate equation (i) w.r.t x

x=2ay’ …(ii)

Now, Divide equation (ii) by (i) , we get

2y=xy’

xy’ - 2y=0

Hence, The required differential equation is xy’ - 2y=0