Question

Show that the order and degree of the differential equation of the family of parabola whose axis is parallel to y-axis is 3 and 1 respectively.

Answer 1

$y=a{x}^2+bx+c$
$\frac{dy}{dx}=2ax+b$
$\frac{d^{2}y}{d{x}^2}=2a$

$\Rightarrow \frac{d^{3}y}{d{x}^3}=0$
Hence order 3, degree 1