Transformations $z\left(t\right)=L\left(t\right)y\left(\varphi \right(t\left)\right)$ of ordinary differential equations

Tryhuk, Václav. "Transformations $z(t)=L(t)y(\varphi (t))$ of ordinary differential equations." Czechoslovak Mathematical Journal 50.3 (2000): 519-529. <http://eudml.org/doc/30580>.

@article{Tryhuk2000,
abstract = {The paper describes the general form of an ordinary differential equation of an order $n+1$$(n\ge 1)$ which allows a nontrivial global transformation consisting of the change of the independent variable and of a nonvanishing factor. A result given by J. Aczél is generalized. A functional equation of the form \[ f\biggl (s, w\_\{00\}v\_0, \ldots , \sum \_\{j=0\}^n w\_\{n j\}v\_j\biggr )=\sum \_\{j=0\}^n w\_\{n+1 j\}v\_j + w\_\{n+1 n+1\}f(x,v, v\_1, \ldots , v\_n), \] where $w_\{n+1 0\}=h(s, x, x_1, u, u_1, \ldots , u_n)$, $ w_\{n+1 1\}=g(s, x, x_1, \ldots , x_n, u, u_1, \ldots , u_n)$ and $w_\{i j\}=a_\{i j\}(x_1, \ldots , x_\{i-j+1\}, u, u_1, \ldots , u_\{i-j\})$ for the given functions $a_\{i j\}$ is solved on $\mathbb \{R\}$, $ u\ne 0.$},
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 = {519-529},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Transformations $z(t)=L(t)y(\varphi (t))$ of ordinary differential equations},
url = {http://eudml.org/doc/30580},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Tryhuk, Václav
TI - Transformations $z(t)=L(t)y(\varphi (t))$ 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 - 519
EP - 529
AB - The paper describes the general form of an ordinary differential equation of an order $n+1$$(n\ge 1)$ which allows a nontrivial global transformation consisting of the change of the independent variable and of a nonvanishing factor. A result given by J. Aczél is generalized. A functional equation of the form \[ f\biggl (s, w_{00}v_0, \ldots , \sum _{j=0}^n w_{n j}v_j\biggr )=\sum _{j=0}^n w_{n+1 j}v_j + w_{n+1 n+1}f(x,v, v_1, \ldots , v_n), \] where $w_{n+1 0}=h(s, x, x_1, u, u_1, \ldots , u_n)$, $ w_{n+1 1}=g(s, x, x_1, \ldots , x_n, u, u_1, \ldots , u_n)$ and $w_{i j}=a_{i j}(x_1, \ldots , x_{i-j+1}, u, u_1, \ldots , u_{i-j})$ for the given functions $a_{i j}$ is solved on $\mathbb {R}$, $ u\ne 0.$
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/30580
ER -