Abstract
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 \(f\left( {s,\upsilon ,w_{11} \upsilon _1 ,...,\sum\limits_{j = 1}^n {w_{nj} \upsilon _j } } \right) = \sum\limits_{j = 1}^n {w_{nj + 1j\upsilon j} + w_{n + 1n + 1} f\left( {x,\upsilon ,\upsilon _1 ,...,\upsilon _n } \right),}\) where \(w_{ij} = a_{ij} \left( {x_1 ,...,x_{i - j + 1} } \right)\) are given functions, \(w_{n + 11} = g\left( {x,x_1 ,...x_n } \right)\) is solved on \(\mathbb{R}\).
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References
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Tryhuk, V. On transformations z(t) = y(ϕ(t)) of ordinary differential equations. Czechoslovak Mathematical Journal 50, 509–518 (2000). https://doi.org/10.1023/A:1022877409091
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DOI: https://doi.org/10.1023/A:1022877409091