ODE book advice

Question

I am in the fourth year of Mathematics and currently taking a course in Ordinary Differential Equations, nonetheless, having a lot of troubles with the course. Mainly because of the book that our proffesor is using for the course: Equações Diferenciais Ordinárias of Jorge Sotomayor.

The book is in Portuguese but that is not the problem. My struggles are due to the fact that I cannot follow the proofs of the book since we entered the third chapter and therefore I do not get the beauty of the theorems neither what the book is trying to build upon those theorems.

These "proofs" are usually not fully explain (many details are left up in the air) and very, honestly very, few comments, and even fewer examples, follow each theorem.

So, I am here to ask you if you know a book for Ordinary Differential Equations with lots of example and comments about the theory the book is developing.

I do not need any good book for ode's, I need a book with a similar content that my course is covering. That is why it seems to me that this is not a duplicate question.

The content of our proffesor's book is:

• First Chapter: Existence and Uniqueness of solutions.
• Second Chapter: Linear Differential Equations
• Third Chapter: Qualitative theory of ODE's: General Aspects. This chapter includes the Tubular Flux Theorem.
• Fourth Chapter: Poincare-Bendixon theorem.
• Fifth Chapter: Stability in the sense of Liapounov.

Thanks in advance.

Answer 1

Part of the desired content can be found in the book Theory of Ordinary Differential Equations by E. A. Coddington and N. Levinson.

• Existence and Uniqueness of solutions: Chapters 1 and 2
• Linear Differential Equations: Chapter 3
• Poincare-Bendixon theorem: Chapter 16
• Stability: Chapter 13

Other books (in French and in English) with similar content, which apparently covers (almost?) all the desired topics, are listed in the references of this course (in Portuguese).