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

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

$\Rightarrow \frac{d^{2}y}{d{x}^2}=0$

Hence, the differential equation is $\frac{d^{2}y}{d{x}^2}=0$