Thieu Vo Ngoc, Franz Winkler,
"Algebraic General Solutions of First Order Algebraic ODEs"
, in Vladimir P. Gerdt, et. al.: Computer Algebraq in Scientific Computing, Serie Lecture Notes in Computer Science, Vol. 9301, Springer International Publishing, Seite(n) 479--492, 2015, ISBN: 0302-9743
Algebraic General Solutions of First Order Algebraic ODEs
Sprache des Titels:
Computer Algebraq in Scientific Computing
In this paper we consider the class of algebraic ordinary differential equations (AODEs), the class of planar rational systems, and discuss their algebraic general solutions. We establish for each parametrizable first order AODE a planar rational system, the associated system, such that one can compute algebraic general solutions of the one from the other and vice versa. For the class of planar rational systems, an algorithm for computing their explicit algebraic general solutions with a given rational first integral is presented. Finally an algorithm for determining an algebraic general solution of degree less than a given positive integer of parametrizable first order AODEs is proposed.