Question

Find the differential equation of all non horizontal line in a plane.

Answer 1

The general equation of all non-horizontal lines in a plane is $ax+by=c$, where $a\ne 0$. differential both sides w.r.t $y$ on both side, we get
$a\frac{dx}{dy}+b=0$
Again, differentiating both sides, w.r.t $y$ we get
$a\frac{d^{2}x}{d{y}^2}=0\Rightarrow \frac{d^{2}x}{d{y}^2}=0$.