I am looking for a large list of ordinary differential equations, as a practice resource.

Preferably the list should be in order of "difficulty" and allow me to practice the different techniques (change of variables, etc).

Do you have a suggestion for a good list like this?

  • 2
    $\begingroup$ For about 12 dollars you can get Schaum's Outline Differential Equations. Amazon has it. I has infinity minus one exercises and lots of worked out examples. I think there is an electronic version. $\endgroup$
    – B. Goddard
    Apr 13, 2017 at 10:42
  • $\begingroup$ a very good book is also by Kamke which can you get by Amazon $\endgroup$ Apr 13, 2017 at 11:07
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    $\begingroup$ Besides the Schaum's Outline book, another book that has a lot of problems with solutions (in the second half of the book) is A Book of Problems in Ordinary Differential Equations (a cheaper copy is here, which is in the famous MIR publishers series of translated Russian books. $\endgroup$ Apr 13, 2017 at 14:15
  • $\begingroup$ I had a chance to look at my copy of the MIR book this weekend (I have the 1983 second printing of the 1981 English translation of the 1978 3rd Russian edition), and I overstated things when I said "with solutions". The book has a lot of worked problems and it has many problems for the student to work (numbered from 1 through 967), but none of problems #1-967 have worked out solutions. However, all of problems #1-967 have answers on pp. 293-326. $\endgroup$ Apr 17, 2017 at 17:59

1 Answer 1


Here are some sources you might want to check out

1.) Problems in Differential Equations by J. L. Brenner. This compact book has 992 DEQs and their solutions (no details - just problem + solution). It is also a Dover book - so the price is great.

2.) Ordinary Differential Equations and Their Solutions by G. M. Murphy. The first half of the book is theory, but the second half has hundreds of problems and their solutions arranged in tables (no details - just problem + solution). Also a Dover book.

3.) Handbook of Exact Solutions for Ordinary Differential Equations 2nd Edition by V. F. Zaitsev and Andrei D. Polyanin. This encyclopedia has over 6000 ODEs and their solution. I do not own this one, but have spent time with it and what is nice is that sometimes it provides useful hints, like use the substitution... What I hate, the cost! Also worth mentioning that there are other books like this that you can search out and maybe even an online one. For example, the one by D. Zwillinger, but also a bunch of others.

4.) As was mentioned in comments (tried and true with many years in existence), Schaum's Outline of Differential Equations, 4th Edition by R. Bronson and G. Costa. This has 563 solved problems (and other practice problems) and is also easy on cost. There is also 2500 Solved Problems in Differential Equations by Richard Bronson. I have referred to my copies on many occasions and they are worth having.

5.) As was mentioned in comments, A Book of Problems in Ordinary Differential Equations by M.L. Krasnov, A.I. Kiselyov, and G.I. Makarenko. This problem book contains exercises that go from easy to challenging. Sadly, it is difficult to find and also to find at a good cost.

6.) A relatively new book is 500 Examples and Problems of Applied Differential Equations by by Ravi P. Agarwal, Simona Hodis, and Donal O’Regan (great price during the Springer Yellow sale).

7.) There is also an online tool that is worth perusing for a source of problems called EqWorld: The World of Mathematical Equations

8.) If you want a truly difficult collection of problems/solutions from a bunch of sources that is collected in a single book, look at the book Problems and Examples in Differential Equations by P. Biler and T. Nadzieja

I suppose it is worth mentioning The Differential Equations Problem Solver by D. R. Arterburn, Staff of Research & Education Association. I have never cared for these and although I own it, I hate the typesetting and also hate trying to locate things in it - so hardly use it, but it has a lot of worked examples.

Lastly, in India, various authors have written many problem books (teach by massive problem solving - an interesting approach that we have abandoned) and you can search those out.


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