2nd Edition

# Handbook of Exact Solutions for Ordinary Differential Equations

816 Pages 4 B/W Illustrations
by Chapman & Hall

816 Pages
by Chapman & Hall

Also available as eBook on:

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 Form F(x,y)y'x = g(x,y) Containing Arbitrary Functions
Equations of the Form F(x,y,y'x) = 0 Containing Arbitrary Functions
SECOND ORDER DIFFERENTIAL EQUATIONS
Linear Equations
Autonomous Equations
Emden-Fowler Equation
Equations of the Form y"xx = A1xn1ym1 + A2xn2ym2
Generalized Emden-Fowler Equation
Equations of the Form y"xx = A1xn1ym1(y'x)l1 + A2xn2ym2(y'x)l2
Equations of the Form y"xx = f(x)g(y)h(y'x)
Some Nonlinear Equations with Arbitrary Parameters
Equations Containing Arbitrary Functions
THIRD ORDER DIFFERENTIAL EQUATIONS
Linear Equations
Equations of the Form y'"xxx = Axαyß(y'x) γ(y"xx)δ
Equations of the Form y'"xxx = f(y)g(y'x)h(y"xx)
Some Nonlinear Equations with Arbitrary Parameters
Nonlinear Equations Containing Arbitrary Functions
FOURTH ORDER DIFFERENTIAL EQUATIONS
Linear Equations
Nonlinear Equations
HIGHER ORDER DIFFERENTIAL EQUATIONS
Linear Equations
Nonlinear Equations
SUPPLEMENTS
Elementary Functions and Their Properties
Special Functions and Their Properties
Table of Indefinite Integrals
REFERENCES
INDEX

### Biography

Valentin F. Zaitsev, Andrei D. Polyanin

"…I have been reading the Polyanin books "Handbook of Linear Partial Differential Equations for Engineers and Scientists" and "Handbook of Exact Solutions for Ordinary Differential Equations". I think these books are extraordinary, and are destined to become classics … CRC Press has provided an invaluable service to science and engineering by publishing these books."
- William Schiesser, Lehigh University

"In summary, this is a very useful and easy-to-read handbook for anyone involved in ordinary differential equations..."
- SIAM Review, 1997, on the first edition

"This best-selling handbook ... is now in its second edition and has been substantially updated and improved ... book is highly recommended for mathematicians, scientists, and
engineers. It would be a useful edition to academic sci-tech libraries, including those that already have the first edition."
- Holly Flynn in E-STREAM