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

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

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

In mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function...

Such an equation is an ordinary differential equation (ODE). A linear differential equation may also be a linear partial differential equation (PDE), if...

differentialium (On the integration of differential equations). A first-order ordinary differential equation in the form: M ( x , y ) d x + N ( x , y...

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...

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...

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

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

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...

developed for the numerical integration of ordinary differential equations (ODEs) and differential algebraic equations (DAEs), to be used. A large number of...

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

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

applications, a Sturm–Liouville problem is a second-order linear ordinary differential equation of the form d d x [ p ( x ) d y d x ] + q ( x ) y = − λ w (...

partial differential equations (SPDEs) generalize partial differential equations via random force terms and coefficients, in the same way ordinary stochastic...

are to solve compared to linear differential equations. This list presents nonlinear ordinary differential equations that have been named, sorted by area...

dynamical system and differential equation topics, by Wikipedia page. See also list of partial differential equation topics, list of equations. Deterministic...

In mathematics, in the theory of ordinary differential equations in the complex plane C {\displaystyle \mathbb {C} } , the points of C {\displaystyle...

In mathematical analysis, Clairaut's equation (or the Clairaut equation) is a differential equation of the form y ( x ) = x d y d x + f ( d y d x ) {\displaystyle...

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...

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

series method is used to seek a power series solution to certain differential equations. In general, such a solution assumes a power series with unknown...

several methods for solving ordinary and partial differential equations, in which algebra allows one to rewrite an equation so that each of two variables...

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

(French: [koʃi]) boundary condition augments an ordinary differential equation or a partial differential equation with conditions that the solution must satisfy...

neural network. In particular, a neural ordinary differential equation (neural ODE) is an ordinary differential equation of the form d h ( t ) d t = f θ ( h...

computing, the trapezoidal rule is a numerical method to solve ordinary differential equations derived from the trapezoidal rule for computing integrals....

to solve inhomogeneous linear ordinary differential equations. For first-order inhomogeneous linear differential equations it is usually possible to find...

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