This report gives the result of running Maple, Mathematica and Sympy on my collection of differential equations.
The following are the software versions used in these tests.
Version 2025 on Linux Arch based.
Version 14.2 on windows 10.
Version 1.13.3 with Python 3.13.1 [GCC 14.2.1 20240910].
The differential equations were collected and stored in sqlite3 database. These were collected from a number of textbooks and other references such as Kamke and Murphy collections. The books used are listed here.
The current number of differential equations is [19474].
Each CAS was given a CPU limit of 3 minutes to solve each ode else the problem is considered not solved and marked as failed.
When Mathematica returns DifferentialRoot as a solution to an ode then this is considered as not solved. Similarly, when Maple returns DESol or ODSESolStruc, then this is also considered as not solved.
If CAS solves the ODE within the timelimit, then it is counted as solved. No verification is done to check if the solution is correct or not.
To reduce the size of latex output, in Maple the command simplify is called on the solution with timeout of 3 minutes. If this times out, then the unsimplified original ode solution is used otherwise the simplified one is used.
Similarly for Mathematica, Simplify is next called. If this times out, then the unsimplified solution is used else the simplified one is used. The time used for simplification is not counted in the CPU time used. The CPU time used only records the time used to solve the ode. (same as with Maple).
Tests are run under windows 10 with 128 GB RAM running on intel i9-12900K 3.20 GHz. For Sympy tests were run under Linux inside a virtual box. Hopefully in the future, the plan is to run all tests on native PC running Linux.