Haysah Yehudah l’kodsho, Yisrael mamsh’losav.

Then the tribe of Yehudah became His holy nation (for jumping into the threatening Yam Suf first), and klal Yisrael became under Hashem’s rule (and no longer under the Egyptians’ rule).

There are numerous opinions in the Gemara, in Maseches P’sachim, as to who authored these chapters of T’hilim (113-118), which comprise what we refer to as “Hallel.” It has been suggested that there is really no dispute in the Gemara. The basic framework was established by the early Prophets and later enhanced by successive generations. Eventually, David HaMelech organized these chapters into the final form we have today in T’hilim (T’shuvah MeiAhavah, Vol. II, responsa 264).

B’tzeis Yisrael miMitzrayim, Beis Yaakov mei’am lo’eiz.

When klal Yisrael [the men] left from the land of Mitzrayim, (and) Beis Yaakov [the women] left from a people of a foreign language (that they did not understand)