# MAX 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 Q(x). 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.

## Enter an homogeneous linear ordinary differential equation

Enter the coefficients a(x),b(x),c(x),d(x) of an equation of of the form
a(x) y'''(x) + b(x) y''(x) + c(x) y'(x) + d(x) y(x) = 0
in the boxes below. Use standard Maple syntax without spaces.

If you receive a syntax error or any other error message, check first how to enter your equation properly.

y'''

y''

y'

y = 0

Independent variable (e.g. x):  (one character only).

Check this box to have the answer also returned as a Maple input string

Check this box to compute only the Galois group of the equation

Last update: 10 December 2004