Αυτή είναι η δική μου μπάλα should also be accepted as correct.
Isn't HellasCad right?
Αυτή είναι η δική μου μπάλα means "this is my own ball".
Yes, but in English you wouldn't say 'This is my own ball!' – you'd say 'This is my ball!', so I think 'Αυτή είναι η δική μου μπάλα!' should be accepted.
We certainly could say "This is my own ball." The kid is leaving school with a ball. And the teacher says: "Don't take the ball home." the child replies "This is my own ball, I brought it from home this morning it doesn't belong to the school."