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Equations can be classified according to the types of operations and quantities involved. Important types include: An algebraic equation or polynomial equation is an equation in which both sides are polynomials (see also system of polynomial equations). These are further classified by degree: linear equation for degree one quadratic equation for degree two cubic equation for degree three quartic equation for degree four quintic equation for degree five A Diophantine equation is an equation where the unknowns are required to be integers A transcendental equation is an equation involving a transcendental function of its unknowns A parametric equation is an equation for which the solutions are sought as functions of some other variables, called parameters appearing in the equations A functional equation is an equation in which the unknowns are functions rather than simple quantities A differential equation is a functional equation involving derivatives of the unknown functions An integral equation is a functional equation involving the antiderivatives of the unknown functions An integro-differential equation is a functional equation involving both the derivatives and the antiderivatives of the unknown functions A difference equation is an equation where the unknown is a function f which occurs in the equation through f(x), f(x−1), …, f(x−k), for some whole integer k called the order of the equation. If x is restricted to be an integer, a difference equation is the same as a recurrence relation |
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