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 = Axyß(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;BR>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 = Axyß(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 INDEXp;lt;BR>Special Functions and Their Properties Table of Indefinite Integrals REFERENCES INDEX.