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

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

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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.
answered May 21, 2014 by meena.p
 

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