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On certain properties of linear iterative equations

Jean-Claude Ndogmo, Fazal Mahomed (2014)

Open Mathematics

An expression for the coefficients of a linear iterative equation in terms of the parameters of the source equation is given both for equations in standard form and for equations in reduced normal form. The operator that generates an iterative equation of a general order in reduced normal form is also obtained and some other properties of iterative equations are established. An expression for the parameters of the source equation of the transformed equation under equivalence transformations is obtained,...

On global transformations of ordinary differential equations of the second order

Václav Tryhuk (2000)

Czechoslovak Mathematical Journal

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 for y 0 , v 0 .

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