Handbook of exact solutions for ordinary differential equations

Abstract

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 yxx = F(y,y'x) Emden-Fowler Equation yxx = Axnym Equations of the Form yxx = A1xn1ym1 + A2xn2ym2 Generalized Emden-Fowler Equation yxx = Axnym(y'x)l Equations of the Form yxx = A1xn1ym1(y'x)l1 + A2xn2ym2(y'x)l2 Equations of the Form yxx = 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(yxx)d Equations of the Form y'xxx = f(y)g(y'x)h(yxx) 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