LOS ANGELES — The composer Matthew Aucoin began working on “Crossing,” his first opera, when he was in college. It was a work of enormous talent, exciting promise and considerable hubris: Mr. Aucoin wrote his own libretto, inventing a story about Walt Whitman’s work with wounded soldiers during the Civil War.

If “Crossing” (2015) lacked “a certain kind of unity” — as Mr. Aucoin, now 29, said in a recent interview — it was still taut, intense and audacious. What would he do next?

The answer came on Saturday, with the premiere of “Eurydice” at Los Angeles Opera, where it runs through Feb. 23 before traveling to the Metropolitan Opera next year. This project demanded a very different approach. Mr. Aucoin didn’t write the libretto; instead, the text was a collaboration with the playwright Sarah Ruhl, closely hewing to her 2003 play, a modern-day take on the Orpheus and Eurydice myth which tells the story from the woman’s perspective.