Question

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

Answer 1

The parabolic equation would be :-

Y=x²

This is the parabolic equation.

Answer 2

Answer:

= xy' - 2y = 0

Step-by-step explanation:

The equation of parabola having vertex at origin and axis along +ve y-axis is

     x² = 4ay ----->(1)     where a is a parameter

Differentiating w.r.t x we get,

         2x = 4a. dy/dx

        x = 2ay'               [ where y' = dy/dx ]

     => a = x / 2y'

 Putting a = x/2y' in (1) we get

  => x² = 4. x/2y . y

  => y' = 2y/x

  => xy' = 2y

   => xy' - 2y = 0

GOOD LUCK !!