A Maple/Aldor Package
for Solving 1st, 2nd and 3rd Order Homogeneous
Linear Ordinary Differential Equations
This page demonstrates the joint use of the Aldor software bernina
with some Maple code
in order to solve 1st, 2nd and 3rd order linear ODEs with coefficients in
The solver is complete in that it will either compute a Liouvillian
solution or prove that there is none.
You can now compute the
Galois group of an equation
without computing a Liouvillian solution (see checkbox below). This is
in particular useful for some 3rd order equations with large finite groups,
for which computing the actual solution still takes a long time.
This feature is complete for irreducible unimodular equations,
for others you get partial information.
Last update: 10 December 2004