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

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

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