Actually I am an undergraduate student of final year and I have to take a course which is $\textit{The theory of ODE}$. Actually I really really do not have any idea about the qualitative thinking of ordinary differential equations and in my undergraduate degree I have taken the courses like real analysis, several variable calculus, basic metric space and topology, little bit of abstract and linear algebra and differential equations. So my question is how to approach with this course and is all the courses that I had taken in previous classes are enough to get into the qualitative study of ODE? And in a previous class when I took differential equation of my core course then I faced difficulties to solve equations and I used to forget the formulas of the ODE's how to solve a given equation. How much this will effect in the course of "Theory of ODE"? Which is the most important and useful prerequisite of this course and my last question is which books I should follow to study ?(Again I am mentioning I am really just a kid of this course and I have very little bit of idea of this course)
Here is the syllabus of the course of "Theory of ODE" that is provided by our university.
