Possible causes for code P0171 combined with P2097on 2004 Dodge Durango 5.7 Hemi

Question

Engine has backfired a couple of times and blow of oil cap. engine has a rough idle.

Answer 1

P0171 Fuel trim lean (Bank 1 Sensor 1)

P2097 Downstream Fuel trim system 1 rich

A lean condition will surely cause a rough idle , but to blow the oil cap off ? False air which are vacuum leak neesds to be check and wrong firing order can cause this, what needs to be ruled out is a mechanical condition such as compression