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Question
Find the differential equation of the family of lines passing through the origin.
Solution
Consider the equation, y = mx, where m is the parameter.
Thus, the above equation represents the family of lines which pass through the origin.
`y=mx....(1)`
`y/x=m....(2)`
Differentiating the above equation (1) with respect to x,
`y = mx`
`dy/dx=m xx1`
`=>dy/dx=m`
`=>dy/dx=y/x` [because from equation 2]
`=>dy/dx-y/x=0`
Thus we have eliminated the constant, m.
The required differential equation is
`dy/dx-y/x=0`
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