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Find the Differential Equation of the Family of Lines Passing Through the Origin. - Mathematics

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Find the differential equation of the family of lines passing through the origin.

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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`

Concept: Formation of a Differential Equation Whose General Solution is Given
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