Displaying similar documents to “Remark to transformations of linear differential and functional-differential equations”

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 for y 0 , v 0 .

On global transformations of functional-differential equations of the first order

Václav Tryhuk (2000)

Czechoslovak Mathematical Journal

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The paper describes the general form of functional-differential equations of the first order with m ( m 1 ) delays which allows nontrivial global transformations consisting of a change of the independent variable and of a nonvanishing factor. A functional equation f ( t , u v , u 1 v 1 , ... , u m v m ) = f ( x , v , v 1 , ... , v m ) g ( t , x , u , u 1 , ... , u m ) u + h ( t , x , u , u 1 , ... , u m ) v for u 0 is solved on and a method of proof by J. Aczél is applied.

On transformations z ( t ) = y ( ϕ ( t ) ) of ordinary differential equations

Václav Tryhuk (2000)

Czechoslovak Mathematical Journal

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The paper describes the general form of an ordinary differential equation of the order n + 1 ( n 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 , ... , j = 1 n w n j v j = j = 1 n w n + 1 j v j + w n + 1 n + 1 f ( x , v , v 1 , ... , v n ) , where w i j = a i j ( x 1 , ... , x i - j + 1 ) are given functions, w n + 1 1 = g ( x , x 1 , ... , x n ) , is solved on .