all solutions of an equation is its solution set. An equation may be solved either numerically or symbolically. Solving an equation numerically means that...

In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with other...

are commonly used for solving differential equations on a computer. A partial differential equation (PDE) is a differential equation that contains unknown...

\end{alignedat}}} One method for solving such a system is as follows. First, solve the top equation for x {\displaystyle x} in terms of y {\displaystyle...

consisting of two expressions related with an equals sign is an equation. Solving an equation containing variables consists of determining which values of...

also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering –...

out X – α. Solving P(x) = 0 thus reduces to solving the degree n – 1 equation Q(x) = 0. See for example the case n = 3. To solve an equation of degree...

improvements these methods cannot solve most Diophantine equations. The difficulty of solving Diophantine equations is illustrated by Hilbert's tenth...

Solving these two linear equations provides the roots of the quadratic. For most students, factoring by inspection is the first method of solving quadratic...

differential equations and integral equations are functional equations. However, a more restricted meaning is often used, where a functional equation is an equation...

equations in quantum mechanics List of equations in nuclear and particle physics Variables commonly used in physics Equation solving Theory of equations...

could not solve this with a compass and straightedge construction, a task which is now known to be impossible. Methods for solving cubic equations appear...

or HHL algorithm is a quantum algorithm for numerically solving a system of linear equations, designed by Aram Harrow, Avinatan Hassidim, and Seth Lloyd...

Mathworld - Quintic Equation – more details on methods for solving Quintics. Solving Solvable Quintics – a method for solving solvable quintics due to David...

Solving the geodesic equations is a procedure used in mathematics, particularly Riemannian geometry, and in physics, particularly in general relativity...

Pell's equation, also called the Pell–Fermat equation, is any Diophantine equation of the form x 2 − n y 2 = 1 , {\displaystyle x^{2}-ny^{2}=1,} where...

faster matrix multiplication Solving systems of linear equations Biconjugate gradient method: solves systems of linear equations Conjugate gradient: an algorithm...

mathematics and physics, the heat equation is a certain partial differential equation. Solutions of the heat equation are sometimes known as caloric functions...

small isolating intervals for real roots or disks for complex roots. Solving an equation f(x) = g(x) is the same as finding the roots of the function h(x)...

The wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields such as mechanical waves...

polynomial equation for which one is interested only in the solutions which are integers is called a Diophantine equation. Solving Diophantine equations is generally...

Engineering Equation Solver (EES) is a commercial software package used for solution of systems of simultaneous non-linear equations. It provides many...

equation solver and library of built-in equations. This feature allows a multi-variable equation to be entered by the user, and the equation solved for...

methods for solving differentiable equations to apply to solving difference equations, and therefore recurrence relations. Summation equations relate to...

Characteristic equation may refer to: Characteristic equation (calculus), used to solve linear differential equations Characteristic equation, the equation obtained...

high-order equations can be solved by “separation” of the unknowns, reducing them to algebraic equations. The following can also be used when solving transcendental...

Divide both sides by 2, This is a cubic equation in y. Solve for y using any method for solving such equations (e.g. conversion to a reduced cubic and...

quadratic equation. Other ways of solving quadratic equations, such as completing the square, yield the same solutions. Given a general quadratic equation of...

enables solving a broader scope of problems. Many quantitative relationships in science and mathematics are expressed as algebraic equations. In mathematics...

an equidimensional equation. Because of its particularly simple equidimensional structure, the differential equation can be solved explicitly. Let y(n)(x)...