In Irodov's Basic Laws of Electromagnetism, D is derived as D=ε°E+P. Later substituting the polarization vector for an isotropic dielectric as P=Χε°E, the result reached is D=ε°εD where ε is dielectric constant of the dielectric.
However later in an example he says that the second result is not valid (in that particular example). See Example 3. Does the invalidity of the second result mean the sphere is not made of a isotropic material? If yes, how do we infer that? Ifnot,then what is the reason behind the invalidity?