Linearization criteria for two-dimensional systems of second-order ordinary differential equations (ODEs) have been derived earlier using complex symmetry analysis. For such systems, the linearizable form, linearization criteria and symmetry group classification are presented. In this paper, we extend the complex approach to obtain a complex-linearizable form of two-dimensional systems of third-order ODEs. This form leads to a linearizable class and linearization criteria of these systems of ODEs.

中文翻译：

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三阶常微分方程二维系统的线性化准则

二维对称二阶常微分方程（ODE）系统的线性化准则已使用复杂对称分析进行了较早的推导。对于此类系统，提出了线性化形式，线性化标准和对称组分类。在本文中，我们扩展了复杂的方法以获得二维线性的三阶ODE系统。这种形式导致这些ODE系统的线性化类别和线性化标准。