Handbook of Exact Solutions for Ordinary Differential EquationsCRC-Press, 9 мая 1995 г. - Всего страниц: 720 Exact solutions have always played and still play an important role in properly understanding the qualitative features of many phenomena. The Handbook of Exact Solutions for Ordinary Differential Equations contains a collection of more than 5,000 ordinary differential equations and their solutions. Coverage focuses on two types of equations: those that are of interest to researchers but are difficult to integrate (Abel equations, Emden-Fowler equations, Painlevé equations, etc.), and equations relevant to applications in heat and mass transfer, nonlinear mechanics, hydrodynamics, nonlinear oscillations, combustion, chemical engineering, and other related fields. The authors also pay special attention to equations containing arbitrary functions, and devote other sections to equations contain one or more arbitrary parameters that the reader can fix at will. |
Содержание
First Order Differential Equations | 6 |
Second Order Differential Equations | 129 |
Trigonometric and Other Functions | 202 |
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A₁ A1 and A2 A₂ Abel equation ae¹² arbitrary arbitrary arccos arcsin arctan Ax)y ax² ay² B₁ Bernoulli equation bx)y bx² C₁ C₂ constant coefficient equation cos(x cos² cosh coth Emden-Fowler equation equation with respect equation with separation Equations Containing exp(Fr² following notation independent variable integrating leads ln² m₁ Mathieu equation modified Bessel functions obtain an equation order linear equation original equation Painlevé Painlevé equation Painlevé transcendent parametric form quadratic equation Riccati equation roots second order equation second order linear separation of variables sin(x sin² sinh solutions of equations Solvable substitution w substitution w(y T₁ tanh transformation upper sign x²y xx Particular solution xxx Solution y'ex y₁ Yxxx