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

Explanation

The equation of family of circles whose centre is on `Y`-axis and radius is `3` unit is
`x^(2)+(y=b)^(2)=9`…….`(1)`
Differentiate equation `(1)` w.r.t.x,
`2x+2(y-b)y'=0`
`implies y-b=-(x)/(y')` ………`(2)`
Put the value of `(y-b)` in equation `(1)` ,
`x^(2)+(-(x)/(y))^(2)=9`
`implies x^(2)[(y')^(2)+11=9(y')^(2)`
`implies (x^(2)-9)(y')^(2)+x^(2)=0`
which is the required differential equation.