That's funny, I (not the poster) didn't stop to think that other readers might not understand the Latin and Greek here!

Both of those forms are third-person and say "may my soul" ( ψυχή/anima) "die with the Philistines". (Definite article in Greek but not in Latin because Latin doesn't have them.)

The original Hebrew has

תָּמוֹת נַפְשִׁי עִם-פְּלִשְׁתִּים

which is also third person "may my soul" (נַפְשִׁי) "die with (the) Philistines".