Survey article highlights symbolic solutions in algebraic differential equations through parametrization techniques.
In this survey article we describe how symbolic computation in algebra and geometry leads to symbolic, i.e., formula solutions of algebraic differential equations. Symbolic solutions of algebraic differential equations can be derived from parametrizations of corresponding algebraic varieties. Such parametrizations in turn can be computed by elimination methods, i.e., methods for solving systems of polynomial equations.
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Franz Winkler (2024) studied this question.