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<p>Over the years, the development of computer algebra has derived enormous benefits for the qualitative theory of ordinary differential equations. In this paper, with the aid of algebraic manipulator-<span>Mathematica</span>, the integrability and linearizability of symmetric planar cubic differential systems are investigated thoroughly. Based on the coefficients and eigenvalues, four simple normal forms are obtained. Furthermore, the integrable and linearizable conditions are classified for each case.</p>

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Symmetric Integrability and Linearizability of Weak Saddles in Planar Cubic Differential Systems

  • 期刊论文

  • 发表日期：

    2025年10月17日

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  • Yusen Wu,
  • Yangtao Li,
  • Xinli Li,
  • Xiangyu Wang

摘要

Over the years, the development of computer algebra has derived enormous benefits for the qualitative theory of ordinary differential equations. In this paper, with the aid of algebraic manipulator-Mathematica, the integrability and linearizability of symmetric planar cubic differential systems are investigated thoroughly. Based on the coefficients and eigenvalues, four simple normal forms are obtained. Furthermore, the integrable and linearizable conditions are classified for each case.