Q. 155.0( 2 Votes )

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

Answer :

When the vertices of parabola at origin and axis along positive y - axis


Then, Equation of parabola is


x2=4ay …(i)


Now, Differentiate equation (i) w.r.t x





x=2ay’ …(ii)


Now, Divide equation (ii) by (i) , we get




2y=xy’


xy’ - 2y=0


Hence, The required differential equation is xy’ - 2y=0


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