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

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

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

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

(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.

(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.

(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.

the equation ̂H𝜓(⃑r)=E𝜓(⃑r), for some constant E; applies to separable solutions 𝛹(⃑r,t)=𝜓(⃑r)𝜙(t) to the Schrödinger equation