Question

The differential equation of all parabolas that have origin as vertex and y-axis as axis of symmetry is ______.

Options

• xy' = 2y

• 2xy' = y

• yy' = 2x

• y" + y = 2x

Answer 1

The differential equation of all parabolas that have origin as vertex and y-axis as axis of symmetry is xy' = 2y.

Explanation:

Equation of parabola is x² = 4ay  ...(i)

Differentiating w.r.t.x we have

2x = 4ay'

⇒ x = 2ay'

⇒ a = `x/(2y^')`

From (i)

⇒ x² = `4 x/(2y^')y`

⇒ xy' = 2y