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Demonstrates geometric properties of symmetries in differential equations, suggesting methods for deriving first integrals.
We provide some geometric properties for -symmetries of system of ordinary differential equations.According to the corresponding geometric representation of -symmetries and solvable structure, we give the first integrals for the system of first-order ordinary differential equations and for the system of n -order ordinary differential equations which has not enough symmetries and -symmetries.
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Zhao et al. (2024) studied this question.
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