Problems and Solutions
             for
             Ordinary Diffferential Equations
             by
             Willi-Hans Steeb
             International School for Scientific Computing
             at
             University of Johannesburg, South Africa
             and
             by
             Yorick Hardy
             Department of Mathematical Sciences
             at
             University of South Africa, South Africa
             updated: February 8, 2017
             Preface
             The purpose of this book is to supply a collection of problems for ordinary
             differential equations.
             Prescribed books for problems.
             1) Continous Symmetries, Lie Algebras, Differential Equations and Com-
             puter Algebra, second edition
             by Willi-Hans Steeb
             World Scientific Publishing, Singapore 2007
             ISBN 981-256-916-2
             http://www.worldscibooks.com/physics/6515.html
             2) Problems and Solutions in Theoretical and Mathematical Physics, third
             edition, Volume I: Introductory Level
             by Willi-Hans Steeb
             World Scientific, Singapore, 2009
             ISBN-13 978-981-4282-14-7
             http://www.worldscibooks.com/physics/7416.html
             3) Problems and Solutions in Theoretical and Mathematical Physics, third
             edition, Volume II: Advanced Level
             by Willi-Hans Steeb
             World Scientific, Singapore, 2009
             ISBN-13 978-981-4282-16-1
             http://www.worldscibooks.com/physics/7416.html
                             v
             The International School for Scientific Computing (ISSC) provides certifi-
             cate courses for this subject. Please contact the author if you want to do
             this course or other courses of the ISSC.
             e-mail addresses of the author:
             steebwilli@gmail.com
             steeb_wh@yahoo.com
             Home page of the author:
             http://issc.uj.ac.za
                             vi
                        Contents
                        Preface                                                      v
                        1 First Order Differential Equations                          1
                        2 Second Order Differential Equations                        22
                        3 First Order Autonomous Systems in the Plane               48
                        4 Higher Order Differential Equations                        67
                        5 Elliptic Functions and Differential Equations             114
                        6 Nonautonomous Systems                                    123
                        7 Hamilton Systems                                         126
                        Bibliography                                               163
                        Index                                                      164
                                                      vii