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

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

The correct answer is option (1) : $\frac{d^2y}{dx^2}=0$

The general equation of all non-vertical lines in a plane is $ax + by = 1, $ where $b ≠0$.

Now,

$ax+ by = 1 $

$⇒a+b \frac{dy}{dx} = 0 $   [ Differentiating w.r.t to x]

$⇒b\frac{d^2y}{dx}= 0 $ [ Differentiating w.r.t to x]

$⇒\frac{d^2y}{dx^2}= 0 $

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