Definitions for differential equation
dif·fer·en·tial equa·tion

Princeton's WordNetRate this definition:0.0 / 0 votes

1. differential equationnoun

   an equation containing differentials of a function

WiktionaryRate this definition:0.0 / 0 votes

1. differential equationnoun

   an equation involving the derivatives of a function

2. Etymology: Coined by Leibniz in 1676.

WikipediaRate this definition:0.0 / 0 votes

1. Differential equation

   In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. 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. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology. Mainly the study of differential equations consists of the study of their solutions (the set of functions that satisfy each equation), and of the properties of their solutions. Only the simplest differential equations are solvable by explicit formulas; however, many properties of solutions of a given differential equation may be determined without computing them exactly. Often when a closed-form expression for the solutions is not available, solutions may be approximated numerically using computers. The theory of dynamical systems puts emphasis on qualitative analysis of systems described by differential equations, while many numerical methods have been developed to determine solutions with a given degree of accuracy.

ChatGPTRate this definition:0.0 / 0 votes

1. differential equation

   A differential equation is a mathematical equation that relates a function with its derivatives. It describes a mathematical relationship where one variable depends upon the rate of change and the value of another variable. They generally represent real-world phenomena that involve change over time, such as physics, engineering, and population modeling.

WikidataRate this definition:0.0 / 0 votes

1. Differential equation

   A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. Differential equations play a prominent role in engineering, physics, economics, and other disciplines. Differential equations arise in many areas of science and technology, specifically whenever a deterministic relation involving some continuously varying quantities and their rates of change in space and/or time is known or postulated. This is illustrated in classical mechanics, where the motion of a body is described by its position and velocity as the time value varies. Newton's laws allow one to express these variables dynamically as a differential equation for the unknown position of the body as a function of time. In some cases, this differential equation may be solved explicitly. An example of modelling a real world problem using differential equations is the determination of the velocity of a ball falling through the air, considering only gravity and air resistance. The ball's acceleration towards the ground is the acceleration due to gravity minus the deceleration due to air resistance. Gravity is considered constant, and air resistance may be modeled as proportional to the ball's velocity. This means that the ball's acceleration, which is a derivative of its velocity, depends on the velocity. Finding the velocity as a function of time involves solving a differential equation.

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1. • Equation

How to pronounce differential equation?

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How to say differential equation in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of differential equation in Chaldean Numerology is: 5

2. Pythagorean Numerology

   The numerical value of differential equation in Pythagorean Numerology is: 4

Examples of differential equation in a Sentence

1. Alan Turing:

   Science is a differential equation. Religion is a boundary condition.

2. Bate, Mueller & White, 1971, "Fundamentals of Astrodynamics":

   Equation (1.2-9) is a second order, nonlinear, vector, differential equation which has defied solution in its present form. It is here therefore we depart from the realities of nature to make some simplifying assumptions...

3. Clifford Truesdell:

   How did Biot arrive at the partial differential equation? [the heat conduction equation] . . . Perhaps Laplace gave Biot the equation and left him to sink or swim for a few years in trying to derive it. That would have been merely an instance of the way great mathematicians since the very beginnings of mathematical research have effortlessly maintained their superiority over ordinary mortals.

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=differential equation
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Differential_Equation
3. ^ Wikipedia
   https://en.wikipedia.org/wiki/Differential_Equation
4. ^ ChatGPT
   https://chat.openai.com
5. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=differential equation