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

Given , ` y = mx +4/m " "` …(i)
` :. (dy)/(dx) = m`
Putting the value of m is Eq. (i) , we get
` y = x ((dy)/(dx))+ 4/(((dy)/(dx))) rArr y ((dy)/(dx)) = x ((dy)/(dx))^(2)+4`
` rArr x ((dy)/(dx))^(2) - y (dy)/(dx) +4 = 0`