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The order of the differential equation is the highest order of derivative of the unknown function that appears in the differential equation. For example, an equation containing only first-order derivatives is a first-order differential equation, an equation containing the second-order derivative is a second-order differential equation, and so on.
Differential equations play a prominent role in many scientific areas: mathematics, physics, engineering, chemistry, biology, medicine, economics, etc. This list presents differential equations that have received specific names, area by area.
A differential equation which may be solved with Bessel functions ... Model of one-dimensional crystal in solid-state physics, Langmuir oscillations in plasma, ...
These include differential equations, manifolds, Lie groups, and ergodic theory. [4] This article gives a summary of the most important of these. This article lists equations from Newtonian mechanics, see analytical mechanics for the more general formulation of classical mechanics (which includes Lagrangian and Hamiltonian mechanics).
Given a simply connected and open subset D of and two functions I and J which are continuous on D, an implicit first-order ordinary differential equation of the form (,) + (,) =,is called an exact differential equation if there exists a continuously differentiable function F, called the potential function, [1] [2] so that
Most elementary and special functions that are encountered in physics and applied mathematics are solutions of linear differential equations (see Holonomic function). When physical phenomena are modeled with non-linear equations, they are generally approximated by linear differential equations for an easier solution.
This is a list of dynamical system and differential equation topics, by Wikipedia page. See also list of partial differential equation topics , list of equations . Dynamical systems, in general
The wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields such as mechanical waves (e.g. water waves, sound waves and seismic waves) or electromagnetic waves (including light waves). It arises in fields like acoustics, electromagnetism, and fluid dynamics.