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

Explanation

To find the differential equation of the family of circles that touch the y-axis at the origin, we can follow these steps:

### Step 1: General Equation of the Circle
The general equation of a circle that touches the y-axis at the origin can be expressed as:
\[ (x - h)^2 + y^2 = r^2 \]
Since the circle touches the y-axis at the origin, the center of the circle must be at \((h, 0)\) where \(h\) is the radius. Therefore, the equation simplifies to:
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