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

1, 2

Equation of required parabola is of the form $y^2=4 a(x-h)$

Differentiating, we have $2 y \frac{d y}{d x}=4 a \Rightarrow y \frac{d y}{d x}=2 a$

Required differential equation $\left(\frac{d y}{d x}\right)^2+\frac{d^2 y}{d x^2} y=0$

Degree of the equation is 1 and order is 2.

Hence (2) is the correct answer.