The search for trivial types

In this paper, we look at strongly minimal sets definable in a differential ly closed field of characteristic 0. In [3], Hrushovski and Sokolovic show that such sets are essentially Zariski geometries. Thus either thre is a de finable strongly minimal field nonorthogonal to D, or D is locally modular and nontrivial. or D is trivial. We show that the strongly minimal sets def ined by a certain family of differential equations are trivial. We also pro ve a theorem wich provides a test for the orthogonality of types over an or dinary differential field.