Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I'm currently working with singular second order differential equations and I'm finding that the standard ODE textbooks available to me aren't very helpful. Most give rote definitions of ordinary/regular points of ODEs, and offer up only the Frobenius method for regular singular points(I'm working with singular, complex ODEs).

Some sources may mention complex analysis/branch cuts. Some may deal with singular ODEs. Some may discuss things geometrically. Nothing so far has mentioned Riemann Surfaces. It's all very disparate, and I find myself lacking a clear understanding of ODEs in the complex plain (and by extension, real valued ODEs as well).

What I'm looking for is an ODE textbook which gives a comprehensive treatment of ODEs in the complex plain, in particular one which discusses second order complex ODEs and their (3 (2?)) singular points. I would also like one which gives a more geometric treatment. Basically, I need a textbook which goes beyond series solutions and gives a general theory of complex (2nd order) ODEs.

Can anyone make any recommendations?

share|cite|improve this question

Maybe Einar Hille's Ordinary differential equations in the complex domain (Google books link)?

(Disclaimer: I haven't read it.)

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.