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 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 involves a multivariable function and one or more of its partial derivatives...

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...

type, a neural ordinary differential equation (neural ODE), defines the evolution of a system's state using an ordinary differential equation whose dynamics...

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

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

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

functions to their derivatives. For example, a first-order matrix ordinary differential equation is x ˙ ( t ) = A ( t ) x ( t ) {\displaystyle \mathbf {\dot...

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...

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...

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

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

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...

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

state, i.e. partial differential equations (PDEs) which are infinite dimensional, as opposed to ordinary differential equations (ODEs) having a finite...

functional differential equation is a differential equation with deviating argument. That is, a functional differential equation is an equation that contains...

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

equation, a first order nonlinear ordinary differential equation Euler conservation equations, a set of quasilinear first-order hyperbolic equations used...

In mathematics, the spectral theory of ordinary differential equations is the part of spectral theory concerned with the determination of the spectrum...

named linear ordinary differential equations. List of nonlinear ordinary differential equations List of nonlinear partial differential equations List of named...

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...

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

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