Question

Find the differential equation of all non-vertical lines in a plane.

Answer 1

Since, the family of all non-vertical line is y=mx+c, where $m\ne tan\frac{\pi }{2}.$
On differentiating w.r.t. x we get
$\frac{dy}{dx}=m$
Again, differentiating w.r.t. x, we get
$\frac{d^{2}y}{d{x}^2}=0$