Handbook of exact solutions for ordinary differential equations
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, Painlev 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.
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First Order Differential Equations
Second Order Differential Equations
Third Order Differential Equations
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2Bxy 2y leads Abel equation aeXx arbitrary arbitrary arbitrary constants arbitrary number arccos arcsin arctan autonomous equation ay leads Bernoulli equation beXx constant coefficient equation cos(Ax cos2 cosh coshx cosx coth e~ax Emden—Fowler equation equation with respect equation with separation Equations Containing Euler equation exp(A2x expf following notation formulae hypergeometric equation independent variable kx leads Legendre transformation lower sign Mathieu equation modified Bessel functions obtain an equation order linear equation original equation Painleve parametric form Particular solution quadratic equation A2 Riccati equation roots second order equation second order linear separation of variables sin(Ax sin2 sinh sinhx sinx solutions of equations substitution w(y tanh th order equation upper sign Weierstrass function ww'x Xuy Xuy xy'm xy'x y'x leads yy'x