Let the centre of the circle on y – axis be (0,b).

We know that the differential equation of the family of circles with centre at (0, b) and radius 3 is: x² + (y- b)² = 3²

⇒ x² + (y- b)² = 9 ----(1)

Now, differentiating both sides w.r.t. x, we get,

2x + 2(y – b).y’ = 0

⇒ (y – b). y’ = x

⇒ y – b =

Thus, substituting the value of ( y – b) in equation (1), we get,

⇒ x²((y’)² + 1) = 9(y’)²

⇒ (x² – 9)(y’)² + x² = 0

Therefore, the required differential equation is (x² – 9)(y’)² + x² = 0