Handbook of Exact Solutions for Ordinary Differential Equations

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ISBN 9781584882978
Cat# C2972

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Features

  • Contains solutions to more than 6200 ODEs-more than any other reference available
  • Offers introductory material describing key concepts, theorems, and methods
  • Pays special attention to equations dependent on arbitrary functions
  • Covers Abel, Emden-Fowler, and Painlevé equations
  • Includes supplemental material on the gamma, beta, Bessel, Legendre, Weierstrass, hypergeometric, and other special functions
  • Summary

    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.
  • Table of Contents

    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

    Editorial Reviews

    "…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