Computer Algebra Independent Differential equations Tests

Nasser M. Abbasi

July 10, 2022   Compiled on July 10, 2022 at 7:58am


 1 Introduction
 2 Text books used
 3 Design of the test program

1 Introduction

These reports show the result of running Maple and Mathematica on my large collection of differential equations. Diagram illustrating the test system is below.

  1. Maple 2022.1 and Mathematica 13.1

    The command used for Maple is

    dsolve(ode,y(x), singsol=all)

    The command used for Mathematica is

    DSolve[ode,y[x],x,IncludeSingularSolutions -> True]

    Each command was given 3 minutes.

    Important note It was found that a number of odes (over 200) now hang in Mathematica 13.1 when using the new option IncludeSingularSolutions -> True but did not hang before when this option was not used.

    The list of these odes are given in this file list_of_odes_that_hang_in_mma_13_1.m.

    The above file can be loaded into Mathematica and used as follows

    listOfOdes = Import["list_of_odes_that_hang_in_mma_13_1.txt", "List"];

    And now each ode in the list can be called using the command

    sol = TimeConstrained[ DSolve[ode, y[x], x, IncludeSingularSolutions -> True], 180];

    (some of the odes have different dependent and independent variable, so the above command need to be adjusted in those cases).

    Therefore the test program was modified to try first with this option and if it timesout, to try again without this option (for a new 3 minutes).

    This option is new in Mathematica V 13.1 and it seems that it needs more work to optimize it.

    Without doing the above, Mathematica 13.1 would have dropped down few percentage points from V 13.01, even though it can actually solve the ode in V 13.1 (but not when using this extra new option).

2 Text books used

The text books used are listed on the page of my own ODE solver at this link ODE solver.

3 Design of the test program

Figure 1: Design of the test program