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# True-or-False: The differential equation of all non horizontal lines in a plane is $\large\frac{d^2y}{dy^2}$$=0. Can you answer this question? ## 1 Answer 0 votes Toolbox: • Equation of a line having slope m is y=mx+c • If the equation has n arbitary constans, then the differential equation will be of n^{th} order The differential equation of all non horizontal lines in a plane is \large\frac{d^2y}{dy^2}$$=0$.
Equation of a non-horizontal line in a plane is $y=mx+c$
When $m$ is a slope
$y=mx+c$
Since there are two arbitrary constants we shall differentiate two times.
Now differentiate with respect to x
$\large\frac{dy}{dx}$$=m Again differentiate with respect to x \large\frac{d^2y}{dx^2}$$=0$
Hence the above statment is $True$
answered May 23, 2013 by