The explican should not be ad hoc, it must be rich in contend. It must have a variety of testable concequances (independent tests or independent evidence) which are different from the explicandum.
For universal laws of nature, they must be independently tested everwhere and at all times. Thus universal laws are testable and falsifiable. An explanation in terms of testable and falsifiable universal laws and initial conditions can be satisfactory.
The aim of science is to find satisfactory explanations or a set of statements that describes the state of affairs to be explained (explicandum). It is aim of science to find satisfactory explanations and by improving the degree of testability by proseeding to better (advanced) testable theories which means proceeding to theories of ever richer content, of higher degrees of universality, and so of higher degrees of precision. This is actual practice of the theoretical science.