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In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with any other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions. [ 1 ]
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. [1] In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two.
Ordinary differential equations occur in many scientific disciplines, including physics, chemistry, biology, and economics. [1] In addition, some methods in numerical partial differential equations convert the partial differential equation into an ordinary differential equation, which must then be solved.
1.6 Ordinary Differential Equations (ODEs) 1.7 Riemannian geometry. 2 Physics. Toggle Physics subsection. 2.1 Astrophysics. 2.2 Classical mechanics. 2.3 Electromagnetism.
Nonlinear ones are of particular interest for their commonality in describing real-world systems and how much more difficult they are to solve compared to linear differential equations. This list presents nonlinear ordinary differential equations that have been named, sorted by area of interest.
In mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta ...
Pages in category "Ordinary differential equations" The following 141 pages are in this category, out of 141 total. This list may not reflect recent changes. ...
To understand uniqueness of solutions, contrast the following two examples of first order ordinary differential equations for y(t). [3] Both differential equations will possess a single stationary point y = 0.
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