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A delay differential equation (also called a differential delay equation or difference-differential equation, although the latter term has a different meaning in the modern ...

If one solution (y_1) to a second-order ordinary differential equation y^('')+P(x)y^'+Q(x)y=0 (1) is known, the other (y_2) may be found using the so-called reduction of ...

A partial differential equation (PDE) is an equation involving functions and their partial derivatives; for example, the wave equation ...

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 ...

The second-order ordinary differential equation (x^2y^')^'+x^2y^n=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 ...

A differential-algebraic equation (DAE) is a type of differential equation in which the derivatives are not (in general) expressed explicitly, and typically derivatives of ...

The second-order ordinary differential equation satisfied by the Neumann polynomials O_n(x).

The ordinary differential equation y^('')+1/2[1/(x-a_1)+1/(x-a_2)+1/(x-a_3)]y^' +1/4[(A_0+A_1x+A_2x^2)/((x-a_1)(x-a_2)(x-a_3))]y=0.

To solve the system of differential equations (dx)/(dt)=Ax(t)+p(t), (1) where A is a matrix and x and p are vectors, first consider the homogeneous case with p=0. The ...