1) well disposed, kind
2) of good cheer, of good courage
Part of Speech: adjective
From G2095 and G2372; in fine spirits, that is, cheerful: - of good cheer, the more cheerfully.
These two sites give similar information, with the definition from several dictionaries and statistics on the use of the word.
Perseus Digital Library
University of Chicago's Logion lexicon
Thayer's dictionary plus other information.
From this site's dictionary (in Italian)
Click on the first column to search for that word as a form of the root εὐθύμως; click on the second column to search for that grammatical form of the root εὐθύμως; click on the third column to search for that word and grammatical form; click on the total to search for the root εὐθύμως.