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

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

The general equation of all non-horizontal lines in $x y$-plane is $a x+b y=1$, where $a \neq 0$.

Now,

$a x+b y=1$

$\Rightarrow a \frac{d x}{d y}+b=0$               [Diff. w.r. to y]

$\Rightarrow a \frac{d^2 x}{d y^2}=0$               [Diff. w.r. to y]

$\Rightarrow \frac{d^2 x}{d y^2}=0$               [∵ a ≠ 0]

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