On April 20, 1995, at 1737 eastern daylight time, a Cessna 172N, N5208D, collided with the terrain while taking off on runway 15 (5,147' x 100') at the Detroit City Airport, Detroit, Michigan, while on a solo instructional flight. Visual meteorological conditions prevailed. The local 14 CFR Part 91 flight was not operating under a flight plan. The airplane was substantially damaged and the student pilot was not injured. The student stated that during the takeoff ground run, the airplane veered to the left. She stated she applied right rudder, however, the airplane continued off the side of the runway. The airplane traveled into the soft grass area where the nose gear collapsed. Inspection of the airplane by a Federal Aviation Administration Inspector failed to reveal any mechanical anomalies which would have resulted in the loss of directional control.