Handbook of Exact Solutions for Ordinary Differential Equations

Part 1 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'2=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. Part 2 Second order differential equations: linear equations autonomous equations y''=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)1 equations of the form y''xx=A1xn1ym1(y'x)11+A2xn2ym2(y'x)12 equations of the form y''xx=f(x)g(y)h(y'x) some nonlinear equations with arbitrary parameters equations containing arbitrary functions. Part 3 Third order differential equations: linear equations equations of the form y'''xxx=Axalphaybeta(y'x)gamma(y''xx)delta 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. Part 4 Fourth order differential equations: linear equations nonlinear equations. Part 5 Higher order differential equations: linear equations nonlinear equations. Part 6 Supplement 1 - some elementary functions and their properties: trigonometric functions hyperbolic functions inverse trigonometric functions inverse hyperbolic functions some conventional symbols. Part 7 Supplement 2 - some special functions: gamma-function Bessel functions Jv and Yv modified Bessel functions Iv and Kv degenerate hypergeometric functions Legendre functions the Weierstrass function.