This collection includes tasks for numerical solution of problems for ordinary differential equations (and systems of equations) on a PC in Mathematica 4. environment. 1. The proposed tasks were tested in 2001/ 2002 academic year on 2-4 courses of the Faculty of Mathematics of VSU. The solution of each problem is accompanied by its verification and clarification of the actual accuracy of the approximate solution built .. For this purpose, a simple original method is proposed .. The first part of the collection gives an example of performing a task with appropriate explanations. More complete comments on the commands used can be found in the reference publications indicated at the end of the collection in the list of recommended literature, as well as directly in the Help. directory. Browser (in English) in the package Mathematica 4. 1