List of named differential equations In mathematics, differential equation is a fundamental concept that is used in many scientific areas. Many of the differential equations that are used have received specific names , which are listed in this article.Pure mathematics So long as the force acting on a particle is known, Newton's second law is sufficient to describe the motion of a particle. Once independent relations for each force acting on a particle are available, they can be substituted into Newton's second law to obtain an ordinary differential equation , which is called the equation of motion . Classical mechanics for particles finds its generalization in continuum mechanics .Electrodynamics are a set of partial differential equations that, together with the Lorentz force law , form the foundation of classical electrodynamics , classical optics , and electric circuits. These fields in turn underlie modern electrical and communications technologies . Maxwell's equations describe how electric and magnetic fields are generated and altered by each other and by charges and currents . They are named after the Scottish physicist and mathematician James Clerk Maxwell , who published an early form of those equations between 1861 and 1862.General relativity The Einstein field equations are a set of ten partial differential equations in Albert Einstein's general theory of relativity which describe the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy . First published by Einstein in 1915 as a tensor equation , the EFE equate local spacetime curvature with the local energy and momentum within that spacetime.Quantum mechanics In quantum mechanics , the analogue of Newton's law is Schrödinger's equation for a quantum system . It is not a simple algebraic equation , but in general a linear partial differential equation , describing the time-evolution of the system's wave function .Fluid dynamics and hydrology Biology and medicine Predator–prey equations The Lotka–Volterra equations , also known as the predator–prey equations , are a pair of first-order, non-linear , differential equations frequently used to describe the population dynamics of two species that interact, one as a predator and the other as prey.Chemistry The rate law or rate equation for a chemical reaction is a differential equation that links the reaction rate with concentrations or pressures of reactants and constant parameters. To determine the rate equation for a particular system one combines the reaction rate with a mass balance for the system. In addition, a range of differential equations are present in the study of thermodynamics and quantum mechanics.Economics and finance
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