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. © 2014 Springer International Publishing.
CITATION STYLE
Grasegger, G., Lastra, A., Sendra, J. R., & Winkler, F. (2014). On symbolic solutions of algebraic partial differential equations. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8660 LNCS, pp. 111–120). Springer Verlag. https://doi.org/10.1007/978-3-319-10515-4_9
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