Form of the differential equation of all family of lines `y=mx+(4)/(m)` by eliminating the arbitrary constant m is

Options

A. `(d^(2)y)/(dx^(2))+0`
B. `x((dy)/(dx))^(2)-y(dy)/(dx)+4=0`
C. `x((dy)/(dx))^(2)+y(dy)/(dx)+4=0`
D. `(dy)/(dx)=0`

Answer

B

Explanation

`y=mx+(4)/(m)` . . . (i)
`therefore(dy)/(dx)=m`
From eq. (i) we get
`y=x((dy)/(dx))+(y)/(((dy)/(dx)))`
`impliesy((dy)/(dx))=x((dy)/(dx))^(2)+4`
`impliesx((dy)/(dx))^(2)-y(dy)/(dx)+4=0`
which is the required differential equation.