The Art of Solving Ordinary Differential Equations: Part One

Odds are you have scratched your head from time to time when you have tried to solve Ordinary Differential Equations. There is an art to doing this effectively and efficiently.
This book is a short introduction to the Art of Solving Ordinary Differential Equations. It is an art because there is no single algorithm that permits you to solve any and all Ordinary Differential Equations, and so you need to have a good sense of the techniques at hand and which ones may be best for the task at hand.
In this book we shall look at some preliminaries when it comes to ODEs, as well what it means to solve an ODE. We shall also look at solving ODE with constant coefficients using a Composite Operator Function P(D).
The change of variables technique will be presented as well as the use of compound functions and integrating functions to solve inexact Ordinary Differential Equations linear in y.
This book includes twenty worked out examples to help you in your understanding of the subject. The worked out examples include several that Pierre de Fermat worked on. There are fifteen book questions you are invited to try your hand at.
In Part Two of the Art of Solving Ordinary Differential Equations we shall look at other techniques such as the series technique and go on to try our hand at solving more complicated differential equations, including coupled systems of equations.
Take your time to understand each example before you continue on into the book. Writing down the examples as you read this little book will help you learn and retain what is being taught.
Enjoy!