Linearization of two second-order ordinary differential equations via fiber preserving point transformations (Q410608)
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scientific article; zbMATH DE number 6021196
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Linearization of two second-order ordinary differential equations via fiber preserving point transformations |
scientific article; zbMATH DE number 6021196 |
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Linearization of two second-order ordinary differential equations via fiber preserving point transformations (English)
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3 April 2012
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Summary: The necessary form of a linearizable system of two second-order ordinary differential equations \(y''_1 = f_1 (x, y_1, y_2, y'_1, y'_2),~ y''_2 = f_2 (x, y_1, y_2, y'_1, y'_2)\) is obtained. Some other necessary conditions are also found. The main problem studied in the paper is to obtain criteria for a system to be equivalent to a linear system with constant coefficients under fiber preserving transformations. A linear system with constant coefficients is chosen because of its simplicity in finding the general solution. Examples demonstrating the procedure of using the linearization theorems are presented.
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