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

Explanation

The equation of family of parabola whose vertex is ar origin and axis is along positive `Y`-axis, is

differenitate w.r.t.x,
`2x=4ay'`……….`(2)`
divide equation `(2)` by equation `(1)`,
`(2x)/(x^(2))=(4ay')/(4ay)`
`implies xy'=2y`
`implies xy'-2y=0`
which is the required differential equation.