# Is there an encyclopedia of DE that accepts solutions?

• jonjacson
In summary: No, I do not. Quantum mechanics equations are quite a different beast. No, I do not. Quantum mechanics equations are quite a different beast.

#### jonjacson

DE= Differential equations.

There is an Encyclopedia of Integer Sequences for example, but I am not able to find the equivalent for DE.

I would like to find a list with all the differential equations that have been solved up to date.

A website or any other source would be interesting. If the source contains the methods to get their solutions would be perfect.

jonjacson said:
DE= Differential equations.

There is an Encyclopedia of Integer Sequences for example, but I am not able to find the equivalent for DE.

I would like to find a list with all the differential equations that have been solved up to date.
I doubt very much that such a list exists.
jonjacson said:
A website or any other source would be interesting. If the source contains the methods to get their solutions would be perfect.

Mark44 said:
I doubt very much that such a list exists.

Maybe if we talk about a specific type of differential equations?

You mean analytic solutions? There are only very few DE's with an analytic solution.

micromass said:
You mean analytic solutions? There are only very few DE's with an analytic solution.

Yes, I mean that. Sorry for not expressing it properly maybe.

Here's a website that has general solutions to a number of common differential equations:

http://eqworld.ipmnet.ru/en/solutions/ode.htm

The page I linked to focuses on ordinary differential equations, but the menu on the left side of the page has links to systems of equations as well as PDEs.

jonjacson
That is what I was looking for. I will purchase those books.

Hopefully they will show the methods employed to find the solutions, I mean methods like the Euler method etc.

eqworld is the best online source. I have the books of Kamke and Murphy, and although they contain a lot of de's with solutions and solution strategies, they are a bit dated. You should mainly use these as a database, not as study material. Much has happened since those books appeared: differential Galois theory, Lie's symmetry analysis, Darboux methods, to name a few. We know more about classification, relationships between DE's, equivalence transformations, etc.

bigfooted said:
eqworld is the best online source. I have the books of Kamke and Murphy, and although they contain a lot of de's with solutions and solution strategies, they are a bit dated. You should mainly use these as a database, not as study material. Much has happened since those books appeared: differential Galois theory, Lie's symmetry analysis, Darboux methods, to name a few. We know more about classification, relationships between DE's, equivalence transformations, etc.
I have the book "ALgorithmic Lie Theory" that talks about another approach to transfering the Galois method to differential equations that was started by Picard and Vessiot. Do you know what is the "state of affairs" on this topic?

Apparently there are several approaches to apply Galois theory to differntial equations, I don't how if that has been completed succesfully and completely.

I also have the book, but I am still in chapter 2. I think it is pretty much the state of affairs regarding Janet bases. I like the algorithmic approach, you can program the algorithm yourself which helps in understanding the method.
There are also people like van der Put and Singer who focus more on linear differential equations, their book is also on my To Do list. On my list is also the thesis of Aistleitner, which gives a nice overview and comparison of some other differential elimination methods
I don't have a complete overview of the current state of affairs, this is all sunday-afternoon math for me, and I am happy to hear of other seminal 'must-read' works.

I don't know when mathematicians consider a mathematical approach to be complete. At least a lot of progress has been made the last 25 years and we can systematically find properties of large classes of differential equations (symmetries, invariant solutions, first integrals).

jonjacson
bigfooted said:
I also have the book, but I am still in chapter 2. I think it is pretty much the state of affairs regarding Janet bases. I like the algorithmic approach, you can program the algorithm yourself which helps in understanding the method.
There are also people like van der Put and Singer who focus more on linear differential equations, their book is also on my To Do list. On my list is also the thesis of Aistleitner, which gives a nice overview and comparison of some other differential elimination methods
I don't have a complete overview of the current state of affairs, this is all sunday-afternoon math for me, and I am happy to hear of other seminal 'must-read' works.

I don't know when mathematicians consider a mathematical approach to be complete. At least a lot of progress has been made the last 25 years and we can systematically find properties of large classes of differential equations (symmetries, invariant solutions, first integrals).

Very interesting.

Do you know if these methods are useful with quantum mechanics equations (Schrodinger)?

I think Lie groups are used in quantum mechanics, but I don't know a lot about it.

jonjacson

## 1. What is an encyclopedia of DE?

An encyclopedia of DE, or differential equations, is a comprehensive reference work that contains information and explanations on various types of differential equations, their properties, and applications.

## 2. Are there any existing encyclopedias of DE?

Yes, there are several encyclopedias of DE that have been published. Some examples include the "Encyclopedia of Differential Equations" by Elsevier and the "Encyclopedia of Mathematics and its Applications" by Cambridge University Press.

## 3. How can I access an encyclopedia of DE?

Many encyclopedias of DE are available in both print and digital formats. They can be purchased from bookstores or accessed through online databases such as JSTOR or SpringerLink.

## 4. Does an encyclopedia of DE accept solutions to problems?

It depends on the specific encyclopedia and its policies. Some encyclopedias may accept solutions submitted by readers, while others may only include solutions provided by the authors or editors of the encyclopedia.

## 5. Is there a specific encyclopedia of DE that is known for accepting solutions?

There is not one specific encyclopedia that is known for accepting solutions, as this may vary depending on the topic and edition. However, some encyclopedias may have a section dedicated to solutions or may offer online supplements with additional solutions to problems.