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Certain traditional methods of Calculus for solving DEs and systems of DEs in engineering analysis depend in one form or another on the use of some general initially assumed analytical representation of the intended solution. Unfortunately this often leads to defining one or several integrals that cannot always be resolved exactly. In order to avoid this complication we propose that the complete "differential" of a general initially assumed analytical representation of the intended solution with unknown coefficients to solve for be used instead as a means of solving for any type of DEs. Such a novel method of differential analysis has led to the development of what appears to be some form of a unified theory of integration. This would represent the greatest opportunity by which the complete Navier-Stokes equations for incompressible flow in the presence of any external forces may be investigated for the existence of any "generalized" analytical solutions under the three most commonly used coordinate systems.
Keywords: Universal Polynomial Transform, ODEs, PDEs, Multinomial Expansion Theorem, Quantum Physics, Quantum computers, Navier-Stokes equations, Theory of everything.

computation;modeling;numerical methods;programming; real-time computation