Question

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

Answer 1

We know that, equation of parabola having vertex at origin and axis along positive y-axis is x² = 4ay, where a is the parameter........(i)

On differentiating Eq. (i) w.r.t. 'x' , we get

On substituting the value of 4a from Eq. (ii) to Eq. (i), we get

or xy' - 2y = 0, which is the required differential equation