In contrast, the case n =2 does not lead to the relation f 0 − − f 1 ′ + f 2 ″ = 0 , since the function f 2 = u 1 need not be differentiable twice. The sufficient condition f 0 − − f 1 ′ + f 2 ″ = 0 is not necessary. Rather, the necessary and sufficient condition may be written as f 0 − − ( f 1 − − f 2 ′ ) ′ = 0 for n =2, f 0 − − ( f 1 − − ( f 2 − − f 3 ′ ) ′ ) ′ = 0 for n =3, and so on; in general, the brackets cannot be opened because of non-differentiability.