Handbook of Exact Solutions for Ordinary Differential Equations

摘要: Part 1 First order differential equations: simplest equations with arbitrary functions integrable in a closed form Riccati - g(y)y'x=f2(x)y2+f1(x)y+f0(x) Abel of the second kind containing polynomial y nonlinear f(x,y)y'2=g(x,y) parameters not solved for derivative F(x,y)y'x=G(x,y) F(x,y,y'x)=0 and functions. 2 Second linear autonomous y''=F(y,y'x) Emden-Fowler equation y''xx=Axnym y''xx=A1xn1ym1+A2xn2ym2 generalized y''xx=Axnym(y'x)1 y''xx=A1xn1ym1(y'x)11+A2xn2ym2(y'x)12 y''xx=f(x)g(y)h(y'x) some 3 Third y'''xxx=Axalphaybeta(y'x)gamma(y''xx)delta y'''xxx=f(y)g(y'x)h(y''xx) 4 Fourth equations. 5 Higher 6 Supplement elementary their properties: trigonometric hyperbolic inverse conventional symbols. 7 special functions: gamma-function Bessel Jv Yv modified Iv Kv degenerate hypergeometric Legendre Weierstrass function.