I don't really have a SOAP (Scripture, Observation, Application, Prayer) today as I can't think of a good application. Daniel 7-8 are prophecies about the upcoming empires after the Babylonian one, and Daniel 8 in particular is a relatively detailed account of the rise and fall of Alexander the Great, followed by the Greek Selucids ruling Palestine -- and culminating in the atrocities of Antiochus Epiphanes. This prophecy is so detailed and clear that liberal scholars who don't believe in prophecy made up the idea that this portion of Daniel must have been written later and added to the book, rather than to acknowledge that God was at work there revealing this to Daniel by the rivers of Babylon.
If you'd like to read about how the Jews rose up and threw out the Selucids and became independent until the rise of Rome, read 1 Maccabees, which can be found in the Septuagint (the Greek translation of the Old Testament which was frequently quoted by the New Testament writers.)
The Psalm passage includes these verses which the late '70s group Boney M popularised:
Beside the rivers of Babylon, we sat and wept as we thought of Jerusalem. We put away our harps, hanging them on the branches of poplar trees. For our captors demanded a song from us. Our tormentors insisted on a joyful hymn: “Sing us one of those songs of Jerusalem!” But how can we sing the songs of the LORD while in a pagan land? [YouTube of By The Rivers of Babylon sung by Boney M]