The dynamic behavior of aeroelastic systems is governed by a complex interaction among inertial, elastic, and aerodynamic forces. To prevent system instability, the interaction among these forces must be properly understood. Accordingly, the present study utilizes the differential transformation method (DTM) to examine the nonlinear dynamic response of a typical aeroelastic system (an aircraft wing) under realistic operating parameters. The system behavior and onset of chaos are interpreted by means of bifurcation diagrams, Poincaré maps, power spectra, and maximum Lyapunov exponent plots. The results reveal the existence of a complex dynamic behavior comprising periodic, quasi-periodic and chaotic responses. It is shown that chaotic motion occurs at specific intervals for different trailing edge and leading edge angles with changing initial conditions. The results presented in this study provide a useful guideline for the design of aircraft wings and confirm the validity of the DTM method as a design and analysis tool for aeroelastic systems in general.