"He's a boy."
Translation:Hogyn ydy o.
dyw/dydy is only used with negative statements where the vetb starts the sentence or clause. See https://www.duolingo.com/skill/cy/Present-3/tips-and-notes and https://www.duolingo.com/skill/cy/Work-1/tips-and-notes.
Hogyn ydy o, Hogyn yw o and various others with yw/ydy in the same position are all valid translations.
bachgen is used in quite a few parts of north-east and mid-Wales where o/fo is the usual masculine pronoun. It is originally a north-east Wales word, apparently.
The rough boundaries between the various dialects are not very consistent when it comes to particular words and phrases.