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

Options

A. `(d^(2)y)/(dx^(2))`
B. `(d^(2)x)/(dy^(2))=0`
C. `(dy)/(dx)=0`
D. `(dx)/(dy)=0`

Answer

B

Explanation

The general equation of all non-horizontal lines in xy-plane is `ax+by=1`, where `a ne 0`.
Now,
`ax+by=1`
`rArr" "a(dx)/(dy)+b=0" [Diff. w.r. to y]"`
`rArr" "a(d^(2)x)/(dy^(2))=0" [Diff. w.r. to y]"`
`rArr" "(d^(2)x)/(dy^(2))=0" "[because a ne 0]`
Hence, the required differential equation is `(d^(2)x)/(dy^(2))=0`