Handbook of Exact Solutions for Ordinary

The second edition of this bestselling handbook contains the solutions for an additional 700 ordinary differential equations (ODEs) and now provides more than 6200 solutions. It also includes a new introductory chapter that describes exact, asymptotic, and approximate analytical methods for solving ODEs, along with basic definitions and discussion of using modern computer algebra systems to solve ODEs. Subsections are now organized into paragraphs, and the rearrangement of equations into these paragraphs allows for an expanded table of contents that helps readers find equations more quickly. More than ever, the handbook is indispensable to a wide range of mathematicians, scientists, engineers, and students.

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 = Ax¿yß(y'x) ¿(y"xx)¿
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
Table of Contents provided by Publisher. All Rights Reserved.

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Handbook of Exact Solutions for Ordinary Differential Equations

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