Solving linear ordinary differential systems in hyperexponential extensions

Moulay A. Barkatou (1) , Clemens Gunter Raab (2)

1 XLIM-DMI - DMI
2 JKU - University of Linz - Johannes Kepler Universität Linz

Let F be a differential field generated from the rational func- tions over some constant field by one hyperexponential ex- tension. We present an algorithm to compute the solutions in Fn of systems of n first-order linear ODEs. Solutions in F of a scalar ODE of higher order can be determined by an algorithm of Bronstein and Fredet. Our approach avoids reduction to the scalar case. We also give examples to show how this can be applied to integration.

Moulay A. Barkatou, Clemens Gunter Raab. Solving linear ordinary differential systems in hyperexponential extensions. ISSAC'12 International Symposium on Symbolic and Algebraic Computation, Jul 2012, Grenoble, France. pp.51-58, ⟨10.1145/2442829.2442841⟩. ⟨hal-00955349⟩