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)
`:. (dy)/(dx)=m`
From Eq. (i) , we get
`y=x""((dy)/(dx))+(4)/((dy//dx))`
`implies y((dy)/(dx))=x((dy)/(dx))^(2)+4 `
`implies x((dy)/(dx))^(2)-y(dy)/(dx)+4=0`
Which is the required differential equation.