Computer Algebra and Polynomials by Jaime Gutierrez Josef Schicho & Martin Weimann

Author:Jaime Gutierrez, Josef Schicho & Martin Weimann
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

In general we might have to apply a linear transformation in order to get a solution of the differential problem. Since contains a transcendental constant, the above solution is a rational general solution of the associated system. This rational general solution of the associated system can be tranformed into a rational general solution of ; in this case

which, after a change of parameter, can be written as .

Of course, not all AODEs are first-order. In [6, 7] Huang, Ngô and Winkler have described how some of these methods can be generalized to AODEs of higher order. Also, one might try to find transformations of the ambient space which transform non-autonomous AODEs into autonomous ones. Indeed, the AODE considered in Example 2.1 can be transformed into the autonomous equation in such a way that the rational solutions are in 1-1 correspondence. A complete characterization of affine transformations preserving rational solvability has been achieved in [10].

In the present paper we investigate a new way of generalizing this solution method. We consider different or more general classes in which we are looking for solutions.

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