(relativity) A symmetric 4 × 4 tensor equation in general relativity in which the gravitational force is described as a curvature of spacetime caused by matter and energy.

plural of ordinary differential equation

(calculus) An equation involving the derivatives of a function of only one independent variable.

(physics) A partial differential equation which describes the conservation of linear momentum for a Newtonian incompressible fluid.

(calculus) A differential equation that involves the partial derivatives of a function of several variables.

(physics) A three-dimensional partial differential equation which determines the evolution of a quantum mechanical wave function

(chemistry) In polymer chemistry, a simple empirical formula that relates molecular weight to the glass transition temperature of a polymer system.

(mathematics) The equation that defines the Legendre polynomials: d/dx[(1-x²)d/dxP_n(x)]+n(n+1)P_n(x)=0.

(mechanics, analytical mechanics) A differential equation which describes a function mathbf q(t) which describes a stationary point of a functional, S( mathbf q)=∫L(t, mathbf q(t), mathbf ̇q(t)),dt, which represents the action of mathbf q(t), with L representing the Lagrangian. The said equation (found through the calculus of variations) is ∂L/∂ mathbf q=d/dt∂L/∂ mathbf ̇q and its solution for mathbf q(t) represents the trajectory of a particle or object, and such trajectory should satisfy the principle of least action.

(physics) An equation that attempts to meld the ideas of quantum mechanics and general relativity. It describes the quantum version of the Hamiltonian constraint using metric variables.