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...

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

regardless of whether known linear functions appear in the equations. In particular, a differential equation is linear if it is linear in terms of the unknown...

differential equations (SDEs) where the progression is random. A linear differential equation is a differential equation that is defined by a linear polynomial...

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

differential equation is homogeneous if it is a homogeneous function of the unknown function and its derivatives. In the case of linear differential equations...

mathematics, a fundamental matrix of a system of n homogeneous linear ordinary differential equations x ˙ ( t ) = A ( t ) x ( t ) {\displaystyle {\dot {\mathbf...

Bernoulli equation is the logistic differential equation. When n = 0 {\displaystyle n=0} , the differential equation is linear. When n = 1 {\displaystyle n=1}...

substantially different. More precisely, consider an ordinary linear differential equation of n-th order f ( n ) ( z ) + ∑ i = 0 n − 1 p i ( z ) f ( i )...

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

In mathematics and physics, a nonlinear partial differential equation is a partial differential equation with nonlinear terms. They describe many different...

or Abel's differential equation identity) is an equation that expresses the Wronskian of two solutions of a homogeneous second-order linear ordinary differential...

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

The equation is also known as the Papperitz equation. The hypergeometric differential equation is a second-order linear differential equation which...

mathematics, a system of differential equations is a finite set of differential equations. Such a system can be either linear or non-linear. Also, such a system...

list of equations. Deterministic system (mathematics) Linear system Partial differential equation Dynamical systems and chaos theory Chaos theory Chaos...

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

The case where the system dynamics are described by a set of linear differential equations and the cost is described by a quadratic function is called...

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

algorithm is a quantum algorithm for numerically solving a system of linear equations, designed by Aram Harrow, Avinatan Hassidim, and Seth Lloyd. The algorithm...

differential equation or difference equation. The characteristic equation can only be formed when the differential equation is linear and homogeneous, and has constant...

known as a linear recurrence relation or linear difference equation) sets equal to 0 a polynomial that is linear in the various iterates of a variable—that...

Schrödinger equation is a linear differential equation in time and position. More precisely, the state of a system is given by a linear combination of...

theory says very roughly that a linear differential equation can be solved by quadratures if and only if its differential Galois group is connected and...

the term partial differential equation, which may be with respect to more than one independent variable. Linear differential equations, which have solutions...

Laguerre's differential equation: x y ″ + ( 1 − x ) y ′ + n y = 0 ,   y = y ( x ) {\displaystyle xy''+(1-x)y'+ny=0,\ y=y(x)} which is a second-order linear differential...

The differential analyser is a mechanical analogue computer designed to solve differential equations by integration, using wheel-and-disc mechanisms to...

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

algebraic Riccati equation. The non-linear Riccati equation can always be converted to a second order linear ordinary differential equation (ODE): If y ′...