"Dyw e ddim yn gallu canu."
Translation:He is not able to sing.
Here, dyw is used because the sentence is negative -- you can't say *Mae e ddim.
A bit like how grammar in English is different between positive statements, negative statements, and questions: you say "He sings" but you don't say "He sings not." or "Sings he?" -- instead, you need "He does not sing" and "Does he sing?"
Similarly in Welsh, positive statements, negative statements, and questions use different forms of the verb bod "to be".
Forms used in negative statements often start with d- as here dyw (also dydy); forms used in questions often with y- (as ydy ...?) though this is sometimes dropped (e.g. you'll hear both dw i ...? and ydw i ...?); and forms used in positive statements can start with r- but this is also sometimes dropped (e.g. rydw i, dw i). Exception: mae doesn't use r-.
Wow, that's a very precise and informative explanation. Thanks for going to the trouble to reply!