Handbook of Exact Solutions for Ordinary Differential Equations (Hardcover, 2)

INTRODUCTION: SOME DEFINITIONS, FORMULAS, METHODS, AND TRANSFORMATIONSFirst-Order Differential EquationsSecond-Order Differential EquationsSecond-Order Nonlinear Differential EquationsLinear Equations o Arbitrary OrderNonlinear Equations of an Arbitrary OrderGroup Methods and Discrete Group AnalysisFIRST ORDER DIFFERENTIAL EQUATIONSSimplest Equations with Arbitrary Functions Integrable in a Closed FormRiccati EquationAbel Equations of the Second KindEquations Containing Polynomial Functions of yEquations of the Form f(x,y)y'x = g(x,y) Containing Arbitrary ParametersEquations of the Form F(x,y,y'x) = 0 Containing Arbitrary ParametersEquations 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 FunctionsSECOND ORDER DIFFERENTIAL EQUATIONSLinear EquationsAutonomous EquationsEmden-Fowler EquationEquations of the Form y"xx = A1xn1ym1 + A2xn2ym2Generalized Emden-Fowler EquationEquations of the Form y"xx = A1xn1ym1(y'x)l1 + A2xn2ym2(y'x)l2Equations of the Form y"xx = f(x)g(y)h(y'x)Some Nonlinear Equations with Arbitrary ParametersEquations Containing Arbitrary FunctionsTHIRD ORDER DIFFERENTIAL EQUATIONSLinear EquationsEquations of the Form y'"xxx = Axαyß(y'x) γ(y"xx)δEquations of the Form y'"xxx = f(y)g(y'x)h(y"xx)Some Nonlinear Equations with Arbitrary ParametersNonlinear Equations Containing Arbitrary FunctionsFOURTH ORDER DIFFERENTIAL EQUATIONSLinear EquationsNonlinear EquationsHIGHER ORDER DIFFERENTIAL EQUATIONSLinear EquationsNonlinear EquationsSUPPLEMENTS Elementary Functions and Their PropertiesSpecial Functions and Their PropertiesTable of Indefinite IntegralsREFERENCESINDEX