DOI: 10.3390/sym15122198 ISSN: 2073-8994

A New Method for Finding Lie Point Symmetries of First-Order Ordinary Differential Equations

Winter Sinkala
  • Physics and Astronomy (miscellaneous)
  • General Mathematics
  • Chemistry (miscellaneous)
  • Computer Science (miscellaneous)

The traditional algorithm for finding Lie point symmetries of ordinary differential equations (ODEs) faces challenges when applied to first-order ODEs. This stems from the fact that for first-order ODEs, unlike higher-order ODEs, the determining equation lacks derivatives, rendering it impossible to decompose into simpler PDEs to be solved for the infinitesimals. Consequently, a common technique for determining Lie point symmetries of first-order ODEs involves making speculative assumptions about the form of the infinitesimal generator. In this study, we propose a novel and more efficient approach for finding Lie point symmetries of first-order ODEs and systems of first-order ODEs. Our method leverages the inherent connection between first-order ODEs and their corresponding second-order counterparts derived through total differentiation. By exploiting this connection, we develop a systematic algorithm for determining Lie point symmetries of a wide range of first-order ODEs. We present the algorithm and provide illustrative examples to demonstrate its effectiveness.

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