The differential equation of the family of parabolas having a vertex at origin and axis along the negative y-axis is given by :

2y-xy'=0 2y'-xy = 0 2y'' - xy' = 0 2y''+ xy' = 0

2y-xy'=0

The general equation of family of parabolas will be \[ { x }^{ 2 } = -4ay\]