Here seems like a good place to mention that according to many poskim, Yom Tov Sheini of Shavuos is more severe in halachah than a regular Yom Tov Sheini. The Chasam Sofer (Shu”t Orach Chaim 145) was asked by R’ Shlomah Kluger the following:
There was a Yid who was deathly ill on the second day of Shavuos who never merited to have any children, and he was worried that his wife would fall to yibbum. It wasn’t a simple case of yibbum, it was a potential shailah of igun [the wife remaining stuck], as the dying husband lived in Brod and his brother lived far away in Rome, and the wife didn’t have enough money to be able to travel there. The lomdim [learned people] wanted to allow the ill husband to write a get [divorce document] and sign it on Yom Tov Sheini of Shavuos for two reasons: 1) Yibbum/chalitzah is a big tikun for the neshomah of the deceased, therefore, certainly when one is still alive and wants to divorce his wife to avoid questions of chalitzah and igun, it is also a big tikun for the neshomah. On Yom Tov Sheini when it comes to taking care of a dead body, we treat the day like weekday, therefore, the same should apply when giving a get, which serves as a tikun for the neshomah. Based on this argument the lomdim wanted to allow a scribe and witnesses to violate Yom Tov Sheini and write a get, which will serve as a great tikun for the dying husband. 2) A second argument they presented was: One is allowed to extinguish a candle on Yom Tov Sheini to save money, therefore, why should writing a get to save a shailah of igun, which a big mitzvah not be allowed.
R’ Shlomah Kluger held that even with these arguments writing a get is still forbidden. The lomdim were very unhappy with this pesak, so they turned to the Chasam Sofer to ask him his opinion on the matter.
The Chasam Sofer writes at great length to show how the pesak of R’ Shlomah Kluger is correct, and cholilah to treat Yom Tov Sheini leniently. At the end of the Teshuvah the Chasam Sofer writes: Yom Tov Sheini of Shavuos is more stringent than a regular Yom Tov Sheini, as Yom Tov Sheini of Shavuos was never enacted due to doubt, as is clear in the Rambam (Hilchos Kiddush HaChodesh 3:12). The reason we normally keep two days Yom Tov in Chutz La’aretz, is because many times the messengers sent out by Beis Din weren’t able to inform people when Rosh Chodesh was, and out of doubt they kept two days. However, when it comes to Shavuos which is always seven weeks after Yom Tov Sheini of Pesach, there is no question when it is, as by the time 49 days have passed from Pesach, everyone knows when Rosh Chodesh Nissan was and when Pesach started. Therefore, when our forefathers kept Shavuos for two days, it wasn’t because they didn’t know when the Yom Tov was, rather, it was because of a lo plug for the other Yomim Tovim [they didn’t differentiate between different Yomim Tovim, to avoid confusing people]. Consequently, since it was kept as two days as a lo plug and not because of doubt, it is more stringent than other Yom Tov Sheini’s.
However, the Shu”t Keren LeDovid (140) asks on the Chasam Sofer that if Yom Tov Sheini of Shavuos is more stringent and is a takonas Chazal, and not kept just because of a doubt, then we should say that an egg born on the first day Shavuos, should be forbidden on the second day of Shavuos like by Rosh Hashanah and we don’t find this to be the halachah.