I’m don’t entirely understand how this question is related to BeagleBoard, since you’re attempting to run an X application on Cygwin. Have you actually installed the XOrg packages which enable Cygwin to do so, and lauched the xorg service? https://x.cygwin.com/docs/ug/setup.html
so, when you export $DISPLAY it’s not complaining about display any more, right?
what exactly happens, though? do you see any graphical output? what gets printed on the stdout of the console from which you run your program?
What is it supposed to do?