Global transformations of linear differential equations.

Neuman, František

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The paper describes the general form of an ordinary differential equation of the second order 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 $f (t, v y, w y + u v z) = f (x, y, z) u^{2} v + g (t, x, u, v, w) v z + h (t, x, u, v, w) y + 2 u w z$ is solved on $ℝ$ for $y \neq 0$ , $v \neq 0 .$