# The differential equation satisfied by all the straight lines in $xy$ plane is

$\begin{array}{1 1}(1)\frac{dy}{dx}=a constant&(2)\frac{d^{2}y}{dx^{2}}=0\\(3)y+\frac{dy}{dx}=0&(4)\frac{d^{2}y}{dx^{2}}+y=0\end{array}$

The equation of the line in the xy plane is
$ax+y+c=0$
$a+ \large\frac{dy}{dx}$$+0 =0 b \large\frac{dy}{dx}$$=-a => \large\frac{dy}{dx}=-\frac{a}{b}$
$\large\frac{d^{2}y}{dx^{2}}=0$
Hence 2 is the correct answer.