"A boy is looking for his dog."
Translation:Chłopiec szuka swojego psa.
'swego' is an example of the... kinda poetic possessive pronouns? They are rather found in songs, poetry and literature than in the everyday language. We only accept them when someone asks for it in a specific sentence. As generally, I think that I could count all the reports of them that I've seen on my fingers :)
If you are interested, you can check the other poetic forms here: https://pl.wiktionary.org/wiki/Aneks:J%C4%99zyk_polski_-_zaimki#m.C3.B3j.2C_tw.C3.B3j.2C_sw.C3.B3j
They are the ones after the slash. They are built in quite a predictable way.