Form the differential equation corresponding to `y^2=a(b-x^2)` by eliminating a and b.

Explanation

`y^2=a(b-x^2) `

Differentiating it with respect to `x`, we get

`2y{dy}/{dx}=-2ax ldots`(1)

Differentiating it with respect to `x`, we get

`({dy}/{dx})^2+y{d^2y}/{dx^2}=-a ldots`(2)

From (1) and (2),

`y{dy}/{dx}=x[({dy}/{dx})^2+y{d^2y}/{dx^2}]`

This is the required differential equation.