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

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

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...

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...

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

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

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...

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

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...

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

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

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

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

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

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

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

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

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

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

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...

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

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

a system can be either a system of ordinary differential equations or a system of partial differential equations. A first-order linear system of ODEs...

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

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

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...

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

characterized as solutions of non-linear ordinary and partial differential equations. The ordinary differential equations for the cases of the normal, Student...