Form the differential equation of all circle touching the x-axis at the origin and centre on the y-axis.

Explanation

To form the differential equation of all circles that touch the x-axis at the origin and have their centers on the y-axis, we can follow these steps:

### Step 1: Determine the general equation of the circle
Since the center of the circle lies on the y-axis, we can denote the center as (0, a), where 'a' is the y-coordinate of the center. The radius of the circle is also 'a', as it touches the x-axis at the origin (0, 0).

The general equation of a circle with center (h, k) and radius r is given by:
\[
(x - h)^2 + (y - k)^2 = r^2
...