A functional transformation approach is presented to aid in the analysis of nonlinear systems of ODEs. This approach differs from traditional linear and numerical methods in that the resulting analytic solutions reveal global information as well as the functionality of system parameters. Solutions to ODEs containing polynomial type nonlinearities are computed in a transform domain using a symbolic programming language. The fundamentals of the method are discussed, followed by two case studies demonstrating the application as well as strengths and weaknesses of the method.