change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent...

with stochastic differential equations (SDEs) where the progression is random. A linear differential equation is a differential equation that is defined...

and parabolic partial differential equations, fluid mechanics, Boltzmann equations, and dispersive partial differential equations. A function u(x, y, z)...

stochastic differential equation now known as Bachelier model. Some of these early examples were linear stochastic differential equations, also called...

the equation are partial derivatives. A linear differential equation or a system of linear equations such that the associated homogeneous equations have...

differentialium (On the integration of differential equations). A first-order ordinary differential equation in the form: M ( x , y ) d x + N ( x , y...

for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their...

equations are special because they are nonlinear differential equations with known exact solutions. A notable special case of the Bernoulli equation is...

system of equations, which is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear...

Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form...

mathematics, an exact differential equation or total differential equation is a certain kind of ordinary differential equation which is widely used in...

leads to a system of ordinary differential equations to which a numerical method for initial value ordinary equations can be applied. The method of lines...

In mathematics, an elliptic partial differential equation is a type of partial differential equation (PDE). In mathematical modeling, elliptic PDEs are...

two kinds of equations: identities and conditional equations. An identity is true for all values of the variables. A conditional equation is only true...

In mathematics, delay differential equations (DDEs) are a type of differential equation in which the derivative of the unknown function at a certain time...

partial differential equations. Laplace's equation is also a special case of the Helmholtz equation. The general theory of solutions to Laplace's equation is...

ordinary differential equations or a system of partial differential equations. A first-order linear system of ODEs is a system in which every equation is first...

solutions of hyperbolic equations are "wave-like". If a disturbance is made in the initial data of a hyperbolic differential equation, then not every point...

A parabolic partial differential equation is a type of partial differential equation (PDE). Parabolic PDEs are used to describe a wide variety of time-dependent...

dynamical system and differential equation topics, by Wikipedia page. See also list of partial differential equation topics, list of equations. Deterministic...

mathematics. Fractional differential equations, also known as extraordinary differential equations, are a generalization of differential equations through the application...

settings, Legendre's differential equation arises naturally whenever one solves Laplace's equation (and related partial differential equations) by separation...

In mathematics, an integro-differential equation is an equation that involves both integrals and derivatives of a function. The general first-order, linear...

classical mechanics, the Euler–Lagrange equations are a system of second-order ordinary differential equations whose solutions are stationary points of...

See also Nonlinear partial differential equation, List of partial differential equation topics and List of nonlinear ordinary differential equations....

Cauchy–Riemann equations, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two partial differential equations which form a necessary...

equation, a first order nonlinear ordinary differential equation Euler conservation equations, a set of quasilinear first-order hyperbolic equations used...

This constraint allows the calculation of the equations of motion of the system using Lagrange's equations. Newton's laws and the concept of forces are...

find the maxima and minima of a function. Equations involving derivatives are called differential equations and are fundamental in describing natural...

an Euler–Cauchy equation, or Cauchy–Euler equation, or simply Euler's equation, is a linear homogeneous ordinary differential equation with variable coefficients...