Find the differential equation of All-ho...

Find the differential equation of All-horizontal lines in a plane. All non-vertical lines in a plane.

Text Solution

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The correct Answer is:

`(d^(2)y)/(dx^(2))=0`

Alll such lines are given by `y=mx+c`.
Here, we have two effective constants m and c. So, it is required to differentiate twice.
`y=mx+c`
`therefore (dy)/(dx)=m`
or `(d^(2)y)/(dx^(2))=0`

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The differential equation of all non- vertical lines in a plane is

`(d^(2)y)/(dx^(2)) = 0`

`(d^(2)x)/(dy^(2)) = 0`

`(dy)/(dx) = 0`

`(dx)/(dy) = 0`

The differential equation of all non-vertical lines in a plane, is

`(d^(2)y)/(dx^(2))=0`

`(d^(2)x)/(dy^(2))=0`

`(dy)/(dx)=0`

`(dx)/(dy)=0`

The differential equation of all non-vertical lines in a plane is

`(d^2y)/(dx^2)=0`

`(d^2x)/(dy^2)=0`