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Home  >>  CBSE XII  >>  Math  >>  Differential Equations
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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$.

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  • 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 meena.p
 

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