Every source I can find of the lyrics of Тополиный пух claims that the song contains the following line near the beginning:
И беспечной птицей в небо улетаешь
If I understand correctly, «беспечной» is declined in the genitive case, which makes sense in the context of the English translation of the lyrics that I found ("[and] like a carefree bird").
However, «птицей» appears to be declined in the instrumental. Why is this the case? Doesn't this break the agreement between the adjective and the noun (as well as not making much sense—"with a bird")?
It's possible that this is simply a transcription error that someone made and every other website copied, as the genitive of птица, птицы, sounds similar (and I can't tell from the audio which one is actually being sung). Additionally, -ей seems to be a common genitive case ending, but it's just the wrong one for птица.
However, I know next to nothing about the Russian language, so I'm not sure whether any of this is accurate. Is this simply an error in the written lyrics, or is there a reason to use the instrumental case for the noun here (or am I wrong about its being in the instrumental at all)?