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I have a 2003 F-150 with appx 140000 miles. For about the last week it has been idling rough in gear when I sit at a light for more than about 20 seconds. The RPMs drop to about 700 then it stalls. It always starts back up immediately but the process starts all over when in drive and idling. I checked the code and it came back P0405. I'm thinking its the DPFE sensor but would like to be sure. Any help is greatly appreciated.
From your description it sounds like the EGR is being held open allowing exhaust gas to flow back into the intake.
Remove the EGR hose, plug the hose and see if the issue goes away for drivability.
If no, the EGR may be stuck open a small amount.
If yes the EVR is stuck partially open allowing vacuum to get to the EGR.
Remove it and do a cleaning so the inside is free to function.
Under the round cap is a filter. Remove the cap, take out the filter and clean it. The filter allows air back in the EGR once it was opened so it will close again.
The DPFE won't cause the drive ability issue because it does not command anything, only reports pressure differences as a test function.
Good luck.