The headword form eu)/i+e is the vocative of an epithet of Dionysus, *eu)/i+os; so at Euripides, Bacchae 413, and elsewhere. The epithet probably derives from the traditional cry of ecstasy eu)oi= (epsilon 3785, epsilon 3787).
The neuter eu)/i+on is attested (e.g. Nonnus, Dionysiaca 15.131) as a substantive in the sense of a Dionysiac song or chant.
For 'inspired' cf. generally epsilon 1364, epsilon 1366.