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...

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

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...

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

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...

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

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

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

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...

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

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

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

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

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

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

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

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...

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

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

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

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

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

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