Restart has fluttery fuel flow.

What is your question?

Just bought the car a few days ago, 131301m, in pretty good condition. Re-starting after driving a while has shown to be an issue. Bad fuel?(I filled it up) Dirty filter? Fuel pump? Exhaust system? It runs fine while driving, city/hwy. Starts cold fine. Check engine light on. No strange sounds.

What makes this problem better or worse?

Re-start is iffy.

How long has your 2005 Cadillac DeVille had this problem?

Just bought it, no idea of history