### 1 Introduction

This report gives the result of running a number of partial diﬀerential equations in Mathematica and Maple. This is work in progress as more PDE’s are being added.

The following systems are used

1. Mathematica 11.3 (64 bit).
2. Maple 2018.2.1 (64 bit) with Physics version MapleCloud 319.

The following are plain text ﬁles of the current collection of the PDE’s used in this report.

Mathematica_PDE_IN_CAS_problems.txt
Maple_PDE_IN_CAS_problems.txt

10 minutes real time was used as the time limit to complete a problem. If CAS did not ﬁnish within this time limit, a failed score is given.

The PC used to run these tests is windows 10 professional 64 bit with 64 GB RAM running Intel core i7-8086K at 4 GHZ.

All possible options, assumptions and HINTS were tried to obtain a solution. The command DSolve was used in Mathematica and the command pdsolve in Maple.

It is possible I missed some option, assumption or HINT, which could help make the CAS able to solve a given PDE now marked as unsolved. Will correct such a case if found. Most of the solutions returned are not veriﬁed. If a CAS returns a solution, it is assumed to be correct and that the problem was solved by CAS.

These problems were collected from textbooks such as

1. Richard Haberman applied partial diﬀerential equations, 5th edition
2. David J Logan applied Partial diﬀerential equations.
3. Partial diﬀerential equations and boundary value problems with Maple by George A. Articolo, 2nd ed.
4. Handbook of ﬁrst order partial diﬀerential equations (HFOPDE), Volume 1, by Polyanin, Zaitsev, Moussiaux (2002).
5. Handbook of nonlinear partial diﬀerential equations (HNPDE), by Polyanin, Zaitsev (2004).

PDE’s from other text books will be added with time.

Some problems were also collected from Maple and Mathematica help pages, documentation and technical forums.

Some of these problems I solved by hand. Will try to add more hand solutions in the future in order to compare with computer solution.
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