Handbook of Exact Solutions for Ordinary Differential Equations [Hardcover]

Exact solutions of differential equations continue to play an important role in the understanding of many phenomena and processes throughout the natural sciences in that they can verify the correctness of or estimate errors in solutions reached by numerical, asymptotic, and approximate analytical methods. The new edition of this bestselling handbook now contains the exact solutions to more than 6200 ordinary differential equations. The authors have made significant enhancements to this edition, including:

An introductory chapter that describes exact, asymptotic, and approximate analytical methods for solving ordinary differential equations

The addition of solutions to more than 1200 nonlinear equations

An improved format that allows for an expanded table of contents that makes locating equations of interest more quickly and easily

Expansion of the supplement on special functions

This handbook's focus on equations encountered in applications and on equations that appear simple but prove particularly difficult to integrate make it an indispensable addition to the arsenals of mathematicians, scientists, and engineers alike.

INTRODUCTION: SOME DEFINITIONS, FORMULAS, METHODS, AND TRANSFORMATIONS
First-Order Differential Equations
Second-Order Differential Equations
Second-Order Nonlinear Differential Equations
Linear Equations o Arbitrary Order
Nonlinear Equations of an Arbitrary Order
Group Methods and Discrete Group Analysis
FIRST ORDER DIFFERENTIAL EQUATIONS
Simplest Equations with Arbitrary Functions Integrable in a Closed Form
Riccati Equation
Abel Equations of the Second Kind
Equations Containing Polynomial Functions of y
Equations of the Form f(x,y)y'x = g(x,y) Containing Arbitrary Parameters
Equations of the Form F(x,y,y'x) = 0 Containing Arbitrary Parameters
Equations of the Foló½