The differential equation of the family 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`
or `a(dx)/(dy)+b=0` [Differentiating w.r.t y]
or `a(d^(2)x)/(dy^(2))=0` [Differentiating w.r.t. y]
or `(d^(2)x)/(dy^(2))=0` `[therefore a ne 0]`
Hence, hte required differential equation is `(d^(2)x)/(dy^(2))=0`