Equation of the family of circles in the second quadrant and touching the coordinate axes

can be represented by

(x – (-a))²+(y – a)²= a², where a is an arbitrary constants.

(1)

Differentiating the above equation with respect to x on both sides, we have,

Substituting the value of a in equation (1)

Rearranging the above equation

This is the required differential equation.