Abstract
The notion of solvable structure is generalized in order to exploit the presence of an \(\mathcal{sl}\)(2, ℝ) algebra of symmetries for a kth-order ordinary differential equation ℰ with k > 3. In this setting, the knowledge of a generalized solvable structure for ℰ allows us to reduce ℰ 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.
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Morando, P., Muriel, C. & Ruiz, A. Generalized Solvable Structures and First Integrals for ODEs Admitting an \(\mathcal{sl}\)(2, ℝ) Symmetry Algebra. J Nonlinear Math Phys 26, 188–201 (2019). https://doi.org/10.1080/14029251.2019.1591712
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DOI: https://doi.org/10.1080/14029251.2019.1591712