Question

Find the differential equation of the family of all non-horizontal lines in a plane 

Answer 1

The equation of the family of non horizontal

Lines in a,plane ax + by = 1, a ≠ 0 and b ∈ R

Given equation is ax + by = 1  .......(1)

Differentiating equation (1) with respect to ‘y’, we get

`"a" ("d"x)/("d"y) + "b"` = 0

∵ 2 arbitrary constant,

∴ Differentiating twice continuously

Again differentiating we get

`"a" ("d"^2x)/("d"y^2)` = 0  ......[∵ a ≠ 0]

`("d"^2x)/("d"y^2)` = 0 is a required differential equation.