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View search results from all Wolfram sites (43051 matches)A functional differential equation is a differential equation in which the derivative y^'(t) of an unknown function y has a value at t that is related to y as a function of ...
The second-order ordinary differential equation y^('')+k/xy^'+epsilony^'y=0.
The second-order ordinary differential equation y^('')+f(x)y^'+y=0.
A difference-differential equation is a two-variable equation consisting of a coupled ordinary differential equation and recurrence equation. In older literature, the term ...
(1) or (2) The solutions are Jacobi polynomials P_n^((alpha,beta))(x) or, in terms of hypergeometric functions, as y(x)=C_1_2F_1(-n,n+1+alpha+beta,1+alpha,1/2(x-1)) ...
The second-order ordinary differential equation y^('')+[(alphaeta)/(1+eta)+(betaeta)/((1+eta)^2)+gamma]y=0, where eta=e^(deltax).
The second-order ordinary differential equation (Moon and Spencer 1961, p. 157; Zwillinger 1997, p. 166).
The ordinary differential equation y^'=-y(1+kappa(x)y)/(1-kappa(x)y).
The ordinary Onsager equation is the sixth-order ordinary differential equation (d^3)/(dx^3)[e^x(d^2)/(dx^2)(e^x(dy)/(dx))]=f(x) (Vicelli 1983; Zwillinger 1997, p. 128), ...
The Abel equation of the first kind is given by y^'=f_0(x)+f_1(x)y+f_2(x)y^2+f_3(x)y^3+... (Murphy 1960, p. 23; Zwillinger 1997, p. 120), and the Abel equation of the second ...
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