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The method of d'Alembert provides a solution to the one-dimensional wave equation (partial^2y)/(partialx^2)=1/(c^2)(partial^2y)/(partialt^2) (1) that models vibrations of a ...

As used in physics, the term "exact" generally refers to a solution that captures the entire physics and mathematics of a problem as opposed to one that is approximate, ...

The discontinuous solution of the surface of revolution area minimization problem for surfaces connecting two circles. When the circles are sufficiently far apart, the usual ...

An equation is said to be a closed-form solution if it solves a given problem in terms of functions and mathematical operations from a given generally-accepted set. For ...

If one solution (y_1) to a second-order ordinary differential equation y^('')+P(x)y^'+Q(x)y=0 (1) is known, the other (y_2) may be found using the so-called reduction of ...

A spiral that gives the solution to the central orbit problem under a radial force law r^..=-mu|r|^(-3)r^^, (1) where mu is a positive constant. There are three solution ...

Kepler's equation gives the relation between the polar coordinates of a celestial body (such as a planet) and the time elapsed from a given initial point. Kepler's equation ...

The S distribution is defined in terms of its distribution function F(x) as the solution to the initial value problem (dF)/(dx)=alpha(F^g-F^h), where F(x_0)=F_0 (Savageau ...

A partial differential equation (PDE) is an equation involving functions and their partial derivatives; for example, the wave equation ...

In the case of a general surface, the distance between two points measured along the surface is known as a geodesic. For example, the shortest distance between two points on ...