Administrative Details
Including grading policy.
Text: Differential Equations with Boundary Value Problems,
by Polking, Boggess, and Arnold (Prentice Hall)
Let's call this text "Bogus" after the second author.
Supplementary Texts: Ordinary Differential Equations,
by E.L. Ince (Dover)
This is a much more old fashioned, more scholarly, and generally deeper text than Bogus. It's also a lot less expensive; check The Poor Man's Library.
You can also learn something about ODEs from Differential Equations and Boundary Value Problems,
Edwards and Penny (Prentice Hall)
Mathematica Notebooks:
Numerically solving an ode and graphing the solution
Draining Cylinders
Euler Approximation
Numerically Solving a System