Form the differential equation of the family of circles having centre on y-axis and radius 3 units.

Explanation

To form the differential equation of the family of circles having their centers on the y-axis and a radius of 3 units, we can follow these steps:

### Step 1: Write the general equation of the circle
The general equation of a circle with center at \((h, k)\) and radius \(r\) is given by:
\[ (x - h)^2 + (y - k)^2 = r^2 \]
In our case, since the center is on the y-axis, we can denote the center as \((0, a)\) where \(a\) is a variable representing the y-coordinate of the center. The radius \(r\) is given as 3. Therefore, the equation of the circle becomes:
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