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Published in:
2014 | OriginalPaper | Chapter
On Symbolic Solutions of Algebraic Partial Differential Equations
Authors : Georg Grasegger, Alberto Lastra, J. Rafael Sendra, Franz Winkler
Published in: Computer Algebra in Scientific Computing
Publisher: Springer International Publishing
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In this paper we present a general procedure for solving first-order autonomous algebraic partial differential equations in two independent variables. The method uses proper rational parametrizations of algebraic surfaces and generalizes a similar procedure for first-order autonomous ordinary differential equations. We will demonstrate in examples that, depending on certain steps in the procedure, rational, radical or even non-algebraic solutions can be found. Solutions computed by the procedure will depend on two arbitrary independent constants.