The required text is
"Elementary Differential Equations and Boundary Value Problems" by William Boyce & Richard DiPrima, John Wiley and Sons, Inc. 2001 IBSN 0 471 31999-6.

The recommended texts, which will be used as sources for some the presented material, and many examples, homework etc. are as follows:

You are expected to learn how to use a software package to solve ordinary differential equations. There are plenty of them, some available on the Internet, some are free of charge, and some are commertial, you may choose any of them. Below is the list of the most popular softwares