Wiktionary
n. (context calculus English) an equation involving the derivatives of a function
WordNet
n. an equation containing differentials of a function
Wikipedia
A differential equation is a mathematical equation that relates some function with its derivatives. In applications, the functions usually represent physical quantities, the derivatives represent their rates of change, and the equation defines a relationship between the two. Because such relations are extremely common, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
In pure mathematics, differential equations are studied from several different perspectives, mostly concerned with their solutions—the set of functions that satisfy the equation. Only the simplest differential equations are solvable by explicit formulas; however, some properties of solutions of a given differential equation may be determined without finding their exact form.
If a self-contained formula for the solution is not available, the solution may be numerically approximated 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.
Usage examples of "differential equation".
The regular, predictable orbital motions of the planets around the Sun, or the Moon around the Earth, were described to high precision by essentially the same differential equation that predicts the swing of a pendulum or the oscillation of a spring.
The margin of error allowed is described by a fourth-order differential equation involving distance, energy, and the angular displacement of charge application away from the lattice axis of the LMT crystal.
The solutions for examples I have given so far implied that we write down and solve a differential equation, so calculus was needed to define the behavior of the solutions.
It is some lesser device--a special-purpose tool like a punched-card reader or Atanasoffs differential equation solver.
When they tried to reproduce mathematically a hyperflight they applied a differential equation of the seventh order.
It was a simple Malthusian Population differential equation, or a damped forced oscillator in engineering terms.
Since we slanted across the magnetic field, you'd need a vectoral differential equation to describe exactly what happened.
She did not know that what her father held on the crumpled sheets of paper was the crude version of a differential equation.
The theory reached him, formulas, specific values of quantities, yes, that particular differential equation would be an absolute bitch to solve.
It's a differential equation, since the rate of loss is a function of the amount of loss, complicated by turbulence.
Reconciling these various aspects of the problem requires the solution of a differential equation of at least order five.
I never watched the cube and she wouldn't know a differential equation if it had reared up and bit her on the butt.