First integrals for time-dependent higher-order Riccati equations by nonholonomic transformation (Q551083)
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scientific article; zbMATH DE number 5920357
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| English | First integrals for time-dependent higher-order Riccati equations by nonholonomic transformation |
scientific article; zbMATH DE number 5920357 |
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First integrals for time-dependent higher-order Riccati equations by nonholonomic transformation (English)
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13 July 2011
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The authors study the first integrals for time-dependent higher-order Riccati equations by nonholonomic transformations. They first introduce the nonholonomic transformation method and use it to compute the first integrals of the time dependent second-order Riccati equation. Then they apply the transformation to compute the first integrals of a class of third-order ordinary differential equations. The authors illustrate the method by several examples.
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nonholonomic transformation
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first integrals
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second-order Riccati equation
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Gambier equation
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numerical examples
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