To find: differential equation of all non-vertical lines

General form of equation of line is given by the equation.

y=mx+c where m is the slope of the line

for the given condition the slope of line cannot be equal to or because if it so then the line will become perpendicular which is not required

so and

now differentiating the general form of equation of line

Formula:

Differentiating it again we get

Therefore, this is the differential equation of all non-vertical lines.