On transformations $z(t)=y(\varphi(t))$ of ordinary differential equations

Title:

On transformations $z(t)=y(\varphi(t))$ of ordinary differential equations

Creator:

Tryhuk, Václav

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:c60415b6-8f01-41f0-b64c-cac0c6613c8a
uuid:c60415b6-8f01-41f0-b64c-cac0c6613c8a

Subject:

ordinary differential equations, linear differential equations, transformations, and functional equations

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

The paper describes the general form of an ordinary differential equation of the order $n+1$ $(n\ge 1)$ which allows a nontrivial global transformation consisting of the change of the independent variable. A result given by J. Aczél is generalized. A functional equation of the form \[ f\biggl (s, v, w_{11}v_{1}, \ldots , \sum _{j=1}^{n}w_{nj}v_{j}\biggr ) = \sum _{j=1}^{n}w_{n+1 j}v_{j} + w_{n+1 n+1}f(x, v, v_{1}, \ldots , v_{n}), \] where $ w_{ij} = a_{ij}(x_{1}, \ldots , x_{i-j+1}) $ are given functions, $ w_{n+1 1} = g(x, x_{1}, \ldots , x_{n})$, is solved on $\mathbb R.$.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

509-518

Source:

Czechoslovak Mathematical Journal | 2000 Volume:50 | Number:3

Harvested from:

CDK

Metadata only:

false