For a first course in ODE, all you really need to know is how to differentiate, integrate, and some basic linear algebra knowledge (taking determinants, how linear transformations etc...)
I've been away from calculus for about 2-3 years (though in the interm have taken other math like analysis and algebra) and I'm preparing to start a course in ODEs next semester, to be followed next year with more courses on dynamical systems and PDEs. I have basically zero experience with DEs. I want to brush up on some calculus skills before the course starts, but I only have a couple weeks to do so. Any suggestion for areas to focus on?