The degree and order of the differential equation of the family of all parabolas whose axis is the $x$ -axis, are respectively:

The equation of a parabola with axis as $x$ -axis is $y^2=4a(x-h)$.There are two arbitrary constants: $a$ and $h$.Thus, the order of the differential equation is 2.Differentiating:$2y{y}^{\prime }=4a⟹y{y}^{\prime }=2a$.Differentiating again:$(y^{\prime }{)}^2+y{y}^{\prime \prime }=0$.The order is 2, and since the highest order derivative $y^{\prime \prime }$ has power 1, the degree is 1.