Q14 of 68 Page 910

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

Equation of the family of parabolas having a vertex at the origin and axis along positive y-axis can be represented by

(x)2 = 4ay, where a is an arbitrary constants.


(1)


Differentiating the above equation with respect to x on both sides, we have,





Substituting the value of a in equation (1)




This is the required differential equation.


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