# Differential-functional equation

From Encyclopedia of Mathematics

An equation relating the argument and the unknown function and its derivatives, generally taken with a functionally transformed argument. Here, the expression of the functional transformation may include the unknown function, as a result of which the equation may contain combinations such as $y'(y(x))$, etc. The concept of a differential-functional equation is often understood to be the synonym of an ordinary differential equation with deviating or distributed arguments (cf. Differential equations, ordinary, with distributed arguments).

#### References

[1] | E. Kamke, "Differentialgleichungen: Lösungen und Lösungsmethoden" , 1. Gewöhnliche Differentialgleichungen , Chelsea, reprint (1947) |

#### Comments

Instead of differential-functional equation one often uses the phrase functional-differential equation.

#### References

[a1] | J.K. Hale, "Functional differential equations" , Springer (1971) |

**How to Cite This Entry:**

Differential-functional equation.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Differential-functional_equation&oldid=40760

This article was adapted from an original article by A.D. Myshkis (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article