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

journal article - other

English

The paper describes the general form of an ordinary differential equation of an order $n+1 (n\geq 1)$, 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 $f(s,w_{00}v_0,\ldots,\sum_{j=0}^n w_{nj}v_j)=\sum_{j=0}^n w_{n+1 j}v_j+w_{n+1 n+1}f(x,v,v_1,\ldots,v_n),$ where $w_{n+1 0}=h(s,x,x_1,u,u_1,\ldots,u_n), w_{n+1 1}=g(s,x,x_1,\ldots,x_n,u,u_1,\ldots,u_{i-j})$ and $w_{ij}=a_{ij}(x_1,\ldots,x_{i-j+1},u,u_1,\ldots,u_{i-j},$ for the given functions $a_{ij}$ is solved on R, $u\neq 0$.

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

519

529

11