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Question -

Form the differential equation of the family of parabolas having vertex at origin and axis along positive y-axis.



Answer -

The equation of the parabola having the vertex at origin and the axis along the positive y-axis is:

Differentiating equation (1) with respect to x, we get:
 
Dividing equation (2) by equation (1), we get:
 
This is the required differential equation.

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