Kamke differential equations using Maple 11 and Mathematica 6

Last update Octt 7,2007 by Nasser Abbasi

Introduction. 1

List of equations. 1

#1 Kamke 1.1. 1

#2 Kamke 1.2. 2

#3 Kamke 1.3. 3

#4 Kamke 1.4. 3

#5 Kamke 1.5. 4

#6 Kamke 1.6. 5

#7 Kamke 1.7. 5

#8 Kamke 1.8. 6

#9 Kamke 1.9. 6

#10 Kamke 1.10. 6

#11 Kamke 1.11. 7

#12 Kamke 1.12. 8

#13 Kamke 1.13. 9

#14 Kamke 1.14. 10

#15 Kamke 1.15. 11

#16 Kamke 1.16. 11

Introduction

On August 15, 2007 I received a copy I ordered from amazon of the book ‘Differential Gleichungen; by Kamke, 3^rd edition. Starting on page 293 up to page 605 it lists many differential equations. I wanted to solve these using Mathematica and Maple and try to compare the results. This started with I saw this web site http://www.cs.uwaterloo.ca/~ecterrab/odetools/comparison.html but it is not up-to-date. So I decided to try to make a new web site which uses latest Maple and Mathematica versions I have.

List of equations

#1 Kamke 1.1

DE		OK?
Maple		Did not solve
Mathematica	Click to enlarge	YES

#2 Kamke 1.2

DE		OK?
Maple		YES
Mathematica		YES

#3 Kamke 1.3

DE		OK?
Maple		YES
Mathematica		YES

#4 Kamke 1.4

DE		OK?
Maple		YES
Mathematica		YES

#5 Kamke 1.5

DE		OK?
Maple		YES
Mathematica		YES (but why definite integral from 1 to x?, it should be indefinite integral? According to text

#6 Kamke 1.6

DE		OK?
Maple		YES
Mathematica		YES

#7 Kamke 1.7

DE		OK?
Maple		YES
Mathematica		YES

#8 Kamke 1.8

DE		OK?
Maple		YES
Mathematica		YES

#9 Kamke 1.9

DE		OK?
Maple		YES
Mathematica		YES

#10 Kamke 1.10

DE		OK?
Maple		YES
Mathematica		YES

#11 Kamke 1.11

DE		OK?
Maple		YES
Mathematica		YES But again MMA uses the definite integral form. See #5 above also.

#12 Kamke 1.12

DE		OK?
Maple		YES Both are correct, maple uses Tanh, and MMA uses Coth. But both miss the solution y=1
Mathematica		YES But also missing solution y=+/- 1

#13 Kamke 1.13

DE		OK?
Maple		Both maple and MMA seems to have the same answer, need more investigation
Mathematica		See above

#14 Kamke 1.14

DE		OK?
Maple		Do not know need more investigation
Mathematica		Do not know need more investigation

#15 Kamke 1.15

DE		OK?
Maple		ok
Mathematica		ok

#16 Kamke 1.16

DE
Maple		Ok?
Mathematica		NO solution