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

Tryhuk, Václav. "On transformations $z(t)=y(\varphi (t))$ of ordinary differential equations." Czechoslovak Mathematical Journal 50.3 (2000): 509-518. <http://eudml.org/doc/30579>.

@article{Tryhuk2000,
abstract = {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 $\mathbb \{R\}.$},
author = {Tryhuk, Václav},
journal = {Czechoslovak Mathematical Journal},
keywords = {ordinary differential equations; linear differential equations; transformations; functional equations; ordinary differential equations; linear differential equations; transformations; functional equations},
language = {eng},
number = {3},
pages = {509-518},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On transformations $z(t)=y(\varphi (t))$ of ordinary differential equations},
url = {http://eudml.org/doc/30579},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Tryhuk, Václav
TI - On transformations $z(t)=y(\varphi (t))$ of ordinary differential equations
JO - Czechoslovak Mathematical Journal
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 50
IS - 3
SP - 509
EP - 518
AB - 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 $\mathbb {R}.$
LA - eng
KW - ordinary differential equations; linear differential equations; transformations; functional equations; ordinary differential equations; linear differential equations; transformations; functional equations
UR - http://eudml.org/doc/30579
ER -