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Question
Find the differential equation of the family of all non-vertical lines in a plane
Solution
The equation of the family of non-vertical lines in a plane ax + by = 1, b ≠ 0, a ∈ R
Given equation is ax + by = 1 ........(1)
Differentiating equation (1) with respect to ‘x’ we get
`"a" + "b" ("d"y)/("d"x)` = 0
∵ 2 arbitrary constant,
∴ Differentiating twice continuously
Again differentiating above equation with respect to ‘x’, we get
`0 + "b" ("d"^2y)/("d"x^2)` = 0
`("d"^2y)/("d"x^2)` = 0 ......[∵ b ≠ 0]
`("d"^2y)/("d"x^2)` = 0 is a required differential equation.
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