Differential equations theorems(Pure mathematics) I'm currently doing some graduate work and came upon some problems. The content of the course is of a pure form with topics such as 


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*Existence and Uniqueness of solutions

*linear system of 1st order ODE

*asympotitic behaviour of soltuions and stability analysis

*boundary value problems for 2nd order ode 


There are a lot of theorems and proofs in the course and I am unable to find a suitable book/books for this type of content. Some of the theorems are as follows 
Theorems
Can anyone point me in the right direction as to what books would be best suitable for content such as this? Solving differential equations is irrelevant here and more emphasis is put on theory and understanding. 

This book by Walter covers the theoretical aspects of ordinary differential equations quite well and was used for my graduate course. 
Also the book by Coddington is often suggested as a good source for rigorous existence and uniqueness theorems. 
I personally find the book by Hale to be rigorous yet not too hard to read. 
