Form the differential equation of the family of circles touching the x-axis at origin.

Explanation

To form the differential equation of the family of circles touching the x-axis at the origin, we can follow these steps:

### Step 1: Understand the Circle's Properties
The circles that touch the x-axis at the origin will have their centers on the y-axis. Let the center of the circle be at the point (0, k), where k is the radius of the circle.

### Step 2: Write the Equation of the Circle
The general equation of a circle with center (0, k) and radius k is given by:
\[
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