Question

Form the differential equation of the family of curves represented by y² = (x – c)³.

Answer 1

y² = (x – c)³

On differentiating the above equation with respect to x we get

Putting the value of (x – c) in the given equation, we get,

On squaring, both sides we get,

Hence, 27y = \(8\left(\frac{dy}{dx}\right)^3\) is the differential equation which represents the family of curves y² = (x – c)³.