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The differential equation of the family of lines $y=mx$ is

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

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$y=mx$
$\large\frac{dy}{dx} $$=m$
$y= \large\frac{dy}{dx}$$.x$
$y.dx= x.dy$
$x.dy -ydx= 0$
ie $y dx -xdy=0$
Hence 2 is the correct answer.
answered May 21, 2014 by meena.p
 

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