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Τι (ποιος) είναι ordinary differential equations - ορισμός

MATHEMATICAL EQUATION INVOLVING DERIVATIVES OF AN UNKNOWN FUNCTION

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Ordinary differential equation

DIFFERENTIAL EQUATION CONTAINING ONE OR MORE FUNCTIONS OF ONE INDEPENDENT VARIABLE AND ITS DERIVATIVES

Ordinary differential equations; Ordinary Differential Equations; Inseparable differential equation; Ordinary Differential Equation; First-order ordinary differential equation; Variable coefficient; Inhomogeneous differential equation; Fundamental system; Ordinary Differential equation; Ordinary differential Equation; System of ordinary differential equations; Implicit differential equation; First order differential equation; Explicit ordinary differential equation; Inhomogeneous ordinary differential equation; First-order differential equation; Non-homogeneous differential equation; First order differential equations; Linear ordinary differential equations; System of ordinary differential equation; Particular integral; List of solvers for ordinary differential equations; List of solvers for ODEs; List of ODE solvers; Particular solution; Software for solving ordinary differential equations; Complementary function

In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and the derivatives of those functions. The term ordinary is used in contrast with the term partial differential equation which may be with respect to more than one independent variable.

https://en.wikipedia.org/wiki/Ordinary_differential_equation

Inseparable differential equation

DIFFERENTIAL EQUATION CONTAINING ONE OR MORE FUNCTIONS OF ONE INDEPENDENT VARIABLE AND ITS DERIVATIVES

Ordinary differential equations; Ordinary Differential Equations; Inseparable differential equation; Ordinary Differential Equation; First-order ordinary differential equation; Variable coefficient; Inhomogeneous differential equation; Fundamental system; Ordinary Differential equation; Ordinary differential Equation; System of ordinary differential equations; Implicit differential equation; First order differential equation; Explicit ordinary differential equation; Inhomogeneous ordinary differential equation; First-order differential equation; Non-homogeneous differential equation; First order differential equations; Linear ordinary differential equations; System of ordinary differential equation; Particular integral; List of solvers for ordinary differential equations; List of solvers for ODEs; List of ODE solvers; Particular solution; Software for solving ordinary differential equations; Complementary function

In mathematics, an inseparable differential equation is an ordinary differential equation that cannot be solved by using separation of variables. To solve an inseparable differential equation one can employ a number of other methods, like the Laplace transform, substitution, etc.

https://en.wikipedia.org/wiki/Inseparable_differential_equation

System of differential equations

FINITE SET OF DIFFERENTIAL EQUATIONS TO BE SOLVED SIMULTANEOUSLY

Differential system; Draft:System of differential equations; System of partial differential equations

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

https://en.wikipedia.org/wiki/System_of_differential_equations

Βικιπαίδεια

Differential equation

In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.

Mainly the study of differential equations consists of the study of their solutions (the set of functions that satisfy each equation), and of the properties of their solutions. Only the simplest differential equations are solvable by explicit formulas; however, many properties of solutions of a given differential equation may be determined without computing them exactly.

Often when a closed-form expression for the solutions is not available, solutions may be approximated numerically using computers. The theory of dynamical systems puts emphasis on qualitative analysis of systems described by differential equations, while many numerical methods have been developed to determine solutions with a given degree of accuracy.

https://en.wikipedia.org/wiki/Differential equation