Handbook of Exact Solutions for Ordinary Differential Equations
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Handbook of Exact Solutions for Ordinary Differential Equations

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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.show more

Product details

  • Hardback | 816 pages
  • 180 x 256 x 50mm | 1,719.11g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • Revised
  • 2nd Revised edition
  • 4 black & white illustrations, 31 black & white tables
  • 1584882972
  • 9781584882978
  • 1,566,540

Review quote

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.show more

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 = Axalphayss(y'x) gamma(y"xx)delta 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 INDEXshow more