Question

Find the differential equation corresponding to the family of curves y = c(x – c)², where c is an arbitrary constant.

Answer 1

The given curve is

y = c(x – c)² ...(i)

Differentiating w.r.t. x, we get

(dy/dx) = 2c(x – c) ...(ii)

From Eq. (i) and (ii), we get, c = (1/4y) (dy/dx)²

Put the value of c in Eq. (ii), we get

which is the required differential equation.