The differential equation of all non-horizontal  lines in a plane, 

The general equation of all non-horizontal lines in xy-plane is $ax+by=1,\text{ where }a\ne 0$

Now,

$\begin{array}{r}ax+by=1\\ \Rightarrow a\frac{dx}{dy}+b=0\\ \Rightarrow a\frac{d^{2}x}{d{y}^2}=0\\ \Rightarrow \frac{d^{2}x}{d{y}^2}=0\end{array}$