The current study presents a novel application of integrated intelligent computing solver for numerical treatment of second-order prediction differential models by exploiting the continuous mapping of artificial neural network (ANN) models of differential operators, global/local search optimization competencies of combined genetic algorithms (GAs) and sequential quadratic programming (SQPs), that is, ANNGASQP. Neural network based differential models are arbitrary integrated to formulate merit function in mean squared error sense and merit function globally optimized with GAs aided with local refinements of SQP. The integrated neuro-evolutionary ANNGASQP scheme is implemented on four different numerical examples of the prediction differential models for numerical solution to examine the precision, proficiency, and consistency. The comparison of proposed solutions through ANNGASQP for prediction differential models with available reference results indicate the good agreement with absolute errors around 10−6 to 10−8. The worth of ANNGASQP is further established through near optimal values of performance measures on statistical date for multiple trials.