Displaying similar documents to “Involutive birational transformations of arbitrary complexity in Euclidean spaces”

On global transformations of ordinary differential equations of the second order

Václav Tryhuk (2000)

Czechoslovak Mathematical Journal

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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 ≠ 0 , v ≠ 0 .