Hi guys, holidays are over and I'm back to uni. Currently doing a quick summer course to catch up with one course I missed last year, we're currently doing differential equations. The textbook that I used for calculus last year has one section on DE, and it's not nearly enough. DE's only take up a little of the course I'm doing atm, we're only going to be doing first order seperable DE's, linear first order DE's and linear second order DE's with constant coefficients. However, right after the course ends, I will be taking an actual course on differential equations. So what I'm looking for is a textbook that will fulfill the needs of my current course, and also of the course I am about to take. Topics covered in the actual DE's course are: first order ordinary differential equations (ODEs), higher order ODEs, numerical techniques for solving ODEs, systems of ODEs, series solutions of ODEs, Laplace transforms, Fourier analysis, solution of linear partial differential equations using the method of separation of variables, and D'Alembert's solution of the wave equation. So, in a nutshell, I'm looking for an introductory DE's textbook. Even just a short list of the best ones will do. There are just so many out there that it's kind of hard to pick one for myself.