PC-Mobile is not quite right. It's more complicated than that. There is a long thread at the top of this forum about charging cables that will provide a lot of information.
1. The Axim takes a LOT of power, as much as 1500 mA if the battery is low, the screen is bright and the CPU is set to fast.
2. The Axim has two set of pins for external power, and the circuitry knows which to use.
3. One set assumes you are connected to a USB port and therefore can only use 500 mA of power (the theoretical limit of a USB port) so you can either charge, or use, the Axim, but not both. If you turn the X50 on, it quits charging. If you turn it off, it starts charging again.
4. The other set is for external power and assumes you have the full Dell wall charger power available, 2410 mA. With that, you can run AND use, so it allows you to do that.
5. Some third party cable manufacturers either didn't know that there were two different pins, or ignored them. The result is that not all of them got it right. Their units CLAIM to charge and run, but don't. The symptom is that the screen appears to flicker as the unit shifts from external power to battery power when the external power fails to provide sufficient current and the voltage drops, then brightens when the power suppy recovers and it shifts back to external, only to drive it down again. and again, etc, etc, etc.
So
IF you get a powerful enough DC converter (1.5A for extended battery, 1.2A for standard battery), and IF the cable is properly wired to the right pins, then you can charge and run.
Not many of those exist. Good luck with it. You might do better to get one of those power inverters (
sample) that turn 12Vdc into 120VAC and just use the Dell mains power converter. It's got plenty of spare capacity.
Or you can get a car mount that provides sufficient power. Arkon and Seidio both make them. They aren't cheap, but they do hold the Axim in addition to providing power.