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An initial value problem is a problem that has its conditions specified at some time t=t_0. Usually, the problem is an ordinary differential equation or a partial ...

(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 ordinary differential equation (1) (Byerly 1959, p. 255). The solution is denoted E_m^p(x) and is known as an ellipsoidal harmonic of the first kind, or Lamé function. ...

A quintic surface is an algebraic surface of degree 5. Togliatti (1940, 1949) showed that quintic surfaces having 31 ordinary double points exist, although he did not ...

Simple harmonic motion refers to the periodic sinusoidal oscillation of an object or quantity. Simple harmonic motion is executed by any quantity obeying the differential ...

Given an ordinary differential equation y^'=f(x,y), the slope field for that differential equation is the vector field that takes a point (x,y) to a unit vector with slope ...

The ordinary differential equation z^2y^('')+zy^'+(z^2-nu^2)y=(4(1/2z)^(nu+1))/(sqrt(pi)Gamma(nu+1/2)), where Gamma(z) is the gamma function (Abramowitz and Stegun 1972, p. ...

The van der Pol equation is an ordinary differential equation that can be derived from the Rayleigh differential equation by differentiating and setting y=y^'. It is an ...

Separation of variables is a method of solving ordinary and partial differential equations. For an ordinary differential equation (dy)/(dx)=g(x)f(y), (1) where f(y)is nonzero ...

The Barth sextic is a sextic surface in complex three-dimensional projective space having the maximum possible number of ordinary double points, namely 65. The surface was ...