Pilot Subsequently Advised The Controller That The Engine Had “Stopped” And Declared A “Mayday” Analysis: The pilot departed, requested flight following services from air traffic control while flying at 3,000 ft msl, and was then assigned a transponder code and identified 4 miles east of the departure airport. The airplane climbed on the runway heading for about 4.5 miles before turning north in a continued climb. The pilot subsequently advised the controller that the engine had “stopped” and declared a “mayday” while looking for a place to land.