Handbook of Exact Solutions for Ordinary Differential Equations

Polyanin, Andrei D.; Zaitsev, V. F.

ISBN 10: 0849394384 / ISBN 13: 9780849394386

Editore: CRC-Press, 1995

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Riassunto:

Exact solutions have always played and still play an important role in properly understanding the qualitative features of many phenomena. The Handbook of Exact Solutions for Ordinary Differential Equations contains a collection of more than 5,000 ordinary differential equations and their solutions. Coverage focuses on two types of equations: those that are of interest to researchers but are difficult to integrate (Abel equations, Emden-Fowler equations, Painlevé equations, etc.), and equations relevant to applications in heat and mass transfer, nonlinear mechanics, hydrodynamics, nonlinear oscillations, combustion, chemical engineering, and other related fields. The authors also pay special attention to equations containing arbitrary functions, and devote other sections to equations contain one or more arbitrary parameters that the reader can fix at will.

Contenuti: Annotation
Foreward
Some Remarks and Notation
First Order Differential Equations
Simplest Equations with Arbitrary Functions Integrable in a Closed Form
Riccati Equations: g(y)y'x = f2(x)y2 + f1(x)y + f0(x)
Abel Equations of the Second Kind
Equations Containing Polynomial Functions of y
Nonlinear Equations of the Form f(x,y)y'x = g(x,y) Containing Arbitrary Parameters
Equations Not Solved for Derivative
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 Not Solved for the Derivative and Containing Arbitrary Functions
Second Order Differential Equations
Linear Equations
Autonomous Equations y"xx = F(y,y'x)
Emden-Fowler Equation y"xx = Axnym
Equations of the Form y"xx = A1xn1ym1 + A2xn2ym2
Generalized Emden-Fowler Equation y"xx = Axnym(y'x)l
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 = Axayß(y'x)g(y"xx)d
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
Supplement 1. Some Elementary Functions and Their Properties
Trigonometric Functions
Hyperbolic Functions
Inverse Trigonometric Functions
Inverse Hyperbolic Functions
Some Conventional Symbols
Supplement 2. Some Special Functions
Gamma-Function
Bessel Functions Jn and Yn
Modified Bessel Functions In and Kn
Degenerate Hypergeometric Functions
Legendre Functions
The Weierstrass Function
References
Index

Dati bibliografici

Titolo: Handbook of Exact Solutions for Ordinary ...
Casa editrice: CRC-Press
Data di pubblicazione: 1995
Legatura: Rilegato
Condizione: very_good