In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions...

In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives...

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

In mathematics, a linear differential equation is a differential equation that is linear in the unknown function and its derivatives, so it can be written...

A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution...

A differential equation can be homogeneous in either of two respects. A first order differential equation is said to be homogeneous if it may be written...

for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their...

In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its...

In mathematics, an ordinary differential equation is called a Bernoulli differential equation if it is of the form y ′ + P ( x ) y = Q ( x ) y n , {\displaystyle...

mathematics, a hyperbolic partial differential equation of order n {\displaystyle n} is a partial differential equation (PDE) that, roughly speaking, has...

Neural differential equations are a class of models in machine learning that combine neural networks with the mathematical framework of differential equations...

system of equations, which is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear...

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and...

In mathematics, delay differential equations (DDEs) are a type of differential equation in which the derivative of the unknown function at a certain time...

mathematics, an exact differential equation or total differential equation is a certain kind of ordinary differential equation which is widely used in...

In mathematics, an elliptic partial differential equation is a type of partial differential equation (PDE). In mathematical modeling, elliptic PDEs are...

A parabolic partial differential equation is a type of partial differential equation (PDE). Parabolic PDEs are used to describe a wide variety of time-dependent...

In mathematics, an integro-differential equation is an equation that involves both integrals and derivatives of a function. The general first-order, linear...

for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs). In...

the Helmholtz equation is the eigenvalue problem for the Laplace operator. It corresponds to the elliptic partial differential equation: ∇ 2 f = − k 2...

In mathematics, a stiff equation is a differential equation for which certain numerical methods for solving the equation are numerically unstable, unless...

. Differential equations are subdivided into ordinary differential equations for functions of a single variable and partial differential equations for...

characteristic equation (or auxiliary equation) is an algebraic equation of degree n upon which depends the solution of a given nth-order differential equation or...

an Euler–Cauchy equation, or Cauchy–Euler equation, or simply Euler's equation, is a linear homogeneous ordinary differential equation with variable coefficients...

Otherwise, Euler's equation may refer to a non-differential equation, as in these three cases: Euler–Lotka equation, a characteristic equation employed in mathematical...

a differential-algebraic system of equations (DAE) is a system of equations that either contains differential equations and algebraic equations, or...

In mathematics, a Riccati equation in the narrowest sense is any first-order ordinary differential equation that is quadratic in the unknown function...

differential equation Cauchy–Euler equation Riccati equation Hill differential equation Gauss–Codazzi equations Chandrasekhar's white dwarf equation Lane-Emden...

classical mechanics, the Euler–Lagrange equations are a system of second-order ordinary differential equations whose solutions are stationary points of...

See also Nonlinear partial differential equation, List of partial differential equation topics and List of nonlinear ordinary differential equations....