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

journal article - other

English

The paper describes the general form of an ordinary differential equation of the order $n+1\ (n\geq 1)$ 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 $$ f(s, v, w_{11}v_{1}, \ldots, \sum_{j=1}^{n}w_{nj}v_{j}) = \sum_{j=1}^{n}w_{n+1 j}v_{j} + w_{n+1 n+1}f(x, v, v_{1}, \ldots, v_{n}), $$ 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 $R.$

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

TRYHUK, V.

1. 1. 2000

ČSAV

Praha

0011-4642

Czechoslovak Mathematical Journal

50

125

Czech Republic

509

518

10