Welsh posessives come in two forms. The basic form would be "Dy gath" which has no particular emphasis, but if you add "Di" it is emphasised that it's your cat and not somebody else's. This is the case with all posessives, though for "ei" (his or her) we do often add "hi/o" after the noun even if we aren't emphasising in order to make it clearer that the person we are talking about is a male or female, this is especially true for cases where the mutation doesn't make it clear i.e "Ei gath" is clearly "His cat" and "Ei chath" is clearly "Her cat", but "Ei sbectol" could be "His glasses" or "Her glasses" so then we probably will say "Ei sbectol o" or "Ei sbectol hi".
Lots of people these days say "Cath di", but this is considered incorrect.
Here are all of the pronouns: "Fy X i", "Dy X di", "Ei X o, "Ei X hi", "Ein X ni", "Eich X chi" and "Eu X nhw",
In many areas of Wales, and on Duo, yes, di and du sound the same. In parts of mid and north Wales the vowel sounds do diverge.
However, cath is a feminine noun and so causes a soft mutation of a following adjective:
- cath ddu - a black cat
- dy gath ddu (di) - your black cat (optional di)
- dy gath (di) -your cat
So a mix-up between 'your cat' and 'your black cat' is unlikely.