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The energy dependence for the singlet sector of Parton DistributionsFunctions (PDFs) is described by an entangled pair of ordinary lineardifferential equations. Although there are no closed analytic solutions, it ispossible to provide approximated results depending on the assumptions and themethodology adopted. These results differ in their sub-leading, neglected termsand ultimately they are associated with different treatments of the theoreticaluncertainties. In this work, a novel analytic approach in Mellin space ispresented and different analytic results for the DGLAP evolution atNext-Lowest-Order are compared. Advantages and disadvantages for each solutionare discussed and generalizations to higher orders are addressed.

Analytic Solutions of the DGLAP Evolution and Theoretical Uncertainties