The display resolution depends of the display driver used to your board, the display driver is configured in the HKEY_LOCAL_MACHINE\System\GDI\Drivers\Display registry key, and the resolution registry key depends of this driver, includes how change the supported resolution.
I am attaching a Microsoft link as support, but the best way to know how configure resolution for YOUR BOARD is find the registry keys about the board display driver.
http://msdn.microsoft.com/en-us/library/aa447504.aspx
About write a application is totally possible, but you have to find the registry key that change the resolution first, and make sure that your image saves the registry key changing. Usually the display driver needs to be rebooted (some dont need), in that moment if the image doesnt save your registry changing, when
=the image is rebooted the registry has the same value than before changing
I hope to help you
Mauricio de Sousa Coelho
Software Engineer - Windows CE