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| Introduction: Some Definitions, Formulas, Methods, and Transformations | |
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| First-Order Differential Equations | |
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| Second-Order Differential Equations | |
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| Second-Order Nonlinear Differential Equations | |
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| Linear Equations o Arbitrary Order | |
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| Nonlinear Equations of an Arbitrary Order | |
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| Group Methods and Discrete Group Analysis | |
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| First Order Differential Equations | |
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| Simplest Equations with Arbitrary Functions Integrable in a Closed Form | |
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| Riccati Equation | |
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| Abel Equations of the Second Kind | |
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| Equations Containing Polynomial Functions of y | |
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| Equations of the Form f(x,y)y'x = g(x,y) Containing Arbitrary Parameters | |
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| Equations of the Form F(x,y,y'x) = 0 Containing Arbitrary Parameters | |
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| Equations of the Form F(x,y)y'x = g(x,y) Containing Arbitrary Functions | |
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| Equations of the Form F(x,y,y'x) = 0 Containing Arbitrary Functions | |
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| Second Order Differential Equations | |
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| Linear Equations | |
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| Autonomous Equations | |
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| Emden-Fowler Equation | |
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| Equations of the Form y"xx = A1xn1ym1 + A2xn2ym2 | |
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| Generalized Emden-Fowler Equation | |
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| Equations of the Form y"xx = A1xn1ym1(y'x)l1 + A2xn2ym2(y'x)l2 | |
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| Equations of the Form y"xx = f(x)g(y)h(y'x) | |
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| Some Nonlinear Equations with Arbitrary Parameters | |
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| Equations Containing Arbitrary Functions | |
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| Third Order Differential Equations | |
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| Linear Equations | |
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| Equations of the Form y'"xxx = Ax�y�(y'x) �(y"xx)� | |
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| Equations of the Form y'"xxx = f(y)g(y'x)h(y"xx) | |
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| Some Nonlinear Equations with Arbitrary Parameters | |
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| Nonlinear Equations Containing Arbitrary Functions | |
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| Fourth Order Differential Equations | |
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| Linear Equations | |
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| Nonlinear Equations | |
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| Higher Order Differential Equations | |
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| Linear Equations | |
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| Nonlinear Equations | |
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| Supplements | |
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| Elementary Functions and Their Properties | |
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| Special Functions and Their Properties | |
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| Table of Indefinite Integrals | |
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| References | |
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| Index | |