Rav and Shmuel agree that an egg laid on the first day of Rosh Hashanah is prohibited on the second day.Rabbah explained that from the time of Rabban Yochanan ben Zakkai, the law of the egg changed and it would be permitted on the second day.Rav Yosef argued that nothing changed in the time of Rabban Yochanan ben Zakkai.
Rava: If there’s a dead body on the first day of Yom Tov, it should be buried by gentiles [we permit telling gentiles to do Melacha because of Kvod Hameis]. On the second day, Jews can do everything. This applies also to the days of Rosh Hashanah - though its law is different regarding an egg laid on the first day.
Nehardai: The law of an egg is also the same on Rosh Hashanah. The entire idea of Rosh Hashanah being one Kedusha is based on the possibility that they wouldn’t declare the thirtieth day of Ellul Rosh Hashanah; however Rav Chinena bar Kahana quoted Rav that since the days of Ezra it never happened! [Rashi adds that even the one time that the witnesses came late (016), their testimony was still accepted on the first day, and it was declared Rosh Hashanah, and from then on the witnesses always came earlier in the day. However because of the possibility that witnesses would come late and their testimony would not be accepted until the following day, they always kept two days].
Mar Zutra: A dead body can only be buried by Jews on the second day if he had died on the first day, but if he died on the second day, it can wait.
Rav Ashi: Even if he just died, he is immediately buried, the Chachomim consider the second day like an ordinary weekday with regard to a corpse. One can even cut cloth or branches in order to honor him.
Ravina: Nowadays that the Magi have taken power [they were oppressive to the Jews in Persia], we can no longer do so [we can only avoid working for them because they respect our religious beliefs, but if they see that we’re doing work for a meis they will require us to do work for them as well].
Ravina was sitting in Rav Ashi’s presence on the first day of Rosh Hashanah which fell on Thursday. He noted that Rav Ashi seemed sad and he asked him about it. Rav Ashi explained that he had not made an Eiruv Tavshilin.Ravina: So do it now! Didn’t Rava say: One can make a conditional Eiruv Tavshilin on the first day of Yom Tov [following the principle elaborated on in 007].Rav Ashi: This was said regarding Yom Tov, did Rava say this regarding Rosh Hashanah?Ravina: But Nehardai said an egg is permitted on the second day of Rosh Hashanah just like any other Yom Tov!Rav Mordechai to Ravina: Rav Ashi told me that he doesn’t hold like Nehardai. 
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