The notion of solvable structure is generalized in order to exploit the presence of an algebra of symmetries for a kth-order ordinary differential equation with k > 3. In this setting, the knowledge of a generalized solvable structure for allows us to reduce to a family of second-order linear ordinary differential equations depending on k − 3 parameters. Examples of explicit integration of fourth and fifth order equations are provided in order to illustrate the procedure.

中文翻译：

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承认对称代数的 ODE 的广义可解结构和第一积分

广义可解结构的概念是为了利用 k > 3 的 k 阶常微分方程的对称代数的存在。在这种情况下，广义可解结构的知识允许我们简化为一个族取决于 k − 3 个参数的二阶线性常微分方程。提供了四阶和五阶方程的显式积分示例以说明该过程。