Question

Find the differential equation of the family of 

(i) all non-vertical lines in a plane

(ii) all non-horizontal lines in a plane.

Answer 1

(i) Equation of family of all non-vertical lines is 

y = mx + c (m ≠ 0) 

Differentiate with respect to ‘x’

dy/dx = m ('m' and 'c' are arbitrary constants)

Again, d²y/dx² = 0

(ii) Equation of family of all non-horizontal lines is