If your computer is still in warranty, you better send them to service center for upgrade or you might risk the void of your warranty. I guess it's part of DELL marketing to use only RAM by DELL.
It wouldn't void the warranty if you enquire them about upgrades and send your desktop to the service center for the upgrade requested. (Please correct me If I'm wrong) As what stated in Dell's Limited Warranty Policy :
I couldn't seems to find proper specification of Mesh 3200 AMD 64 computer. May you please guide me to a page which displays/tells the specification of your computer?