SOLUTION:
There is one constant so we differentiate the equation with respect to x only once.
[tex] (x - C)^2 + y^2 = 9 \longrightarrow \text{Eq. 1} [/tex]
[tex] 2(x - C) + 2yy' = 0 [/tex]
[tex] x - C + yy' = 0 [/tex]
[tex] x - C = -yy' \longrightarrow \text{Eq. 2} [/tex]
Substituting Eq. 2 to Eq. 1,
[tex] (-yy')^2 + y^2 = 9 [/tex]
[tex] \therefore \boxed{y^2(y')^2 + y^2 - 9 = 0} [/tex]
