Form the differential equation of the family of curves represented by `y^2=(x-c)^3`.

Explanation

`y^2=(x-c)^3ldots`(1)

Differentiating it with respect to `x`, we get

`2y{dy}/{dx}=3(x-c)^2ldots`(2)

From (1) and (2),

`c=x-3/2y/{{dy}/{dx}}`

Putting value of `c` in (1), we get

`y^2=(x-x-3/2y/{{dy}/{dx}})^3`

`implies 8({dy}/{dx})^3-27y=0`

...