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  • Find the differential equation of all non-vertical lines in a plane.

Find the differential equation of all non-vertical lines in a plane.

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To find: Differential equation of all non vertical lines

 

The general form of equation of line is given by y=mx+c  where, m is the slope of the line

 

The slope of the line cannot be \frac{\pi}{2} or \frac{3\pi}{2} for the given condition, because if it is, the line will become perpendicular without any necessity.

So,

m\neq \frac{\pi}{2},m\neq \frac{3\pi}{2}

Differentiate the general form of equation of line

\frac{dy}{dx}=m

Formula:

\frac{d(ax)}{dx}=a

Differentiating it again, it becomes:

\frac{d^{2}y}{dx^{2}}=0

Thus, we get the differential equation of all non-vertical lines.

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infoexpert24

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