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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 y"xx = F(y,y'x)
Emden-Fowler Equation y"xx = Axnym
Equations of the Form y"xx = A1xn1ym1 + A2xn2ym2
Generalized Emden-Fowler Equation y"xx = Axnym(y'x)l
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 = Axayß(y'x)g(y"xx)d
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
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
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