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