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A neuro-heuristic scheme is design to solve nonlinear singular second order system based on Thomas-Fermi equation using the strength of universal approximation capabilities of feedforward artificial neural networks supported with optimization power of genetic algorithms and sequential quadratic programming. An error function is constructed by differential equations artificial neural networks and optimization of design parameters of networks is carried out initially with genetic algorithms for the global search while sequential quadratic programming algorithm is used for further rapid local refinements. The performance of the design is analyzed by solving variants of Thomas-Fermi equation. Comparison of the results with standard numerical as well as analytical solvers establish the significance of the method on the basis of accuracy and convergence through statistical performance indices.