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- W2022204966 abstract "By use of the Lie symmetry group methods we analyze the relationship between the first integrals of the simplest linear third-order ordinary differential equations (ODEs) and their point symmetries. It is well known that there are three classes of linear third-order ODEs for maximal cases of point symmetries which are 4, 5, and 7. The simplest scalar linear third-order equation has seven-point symmetries. We obtain the classifying relation between the symmetry and the first integral for the simplest equation. It is shown that the maximal Lie algebra of a first integral for the simplest equation<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:mrow><mml:msup><mml:mi>y</mml:mi><mml:mo>′′′</mml:mo></mml:msup><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math>is unique and four-dimensional. Moreover, we show that the Lie algebra of the simplest linear third-order equation is generated by the symmetries of the two basic integrals. We also obtain counting theorems of the symmetry properties of the first integrals for such linear third-order ODEs. Furthermore, we provide insights into the manner in which one can generate the full Lie algebra of higher-order ODEs of maximal symmetry from two of their basic integrals." @default.
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- W2022204966 date "2013-01-01" @default.
- W2022204966 modified "2023-09-27" @default.
- W2022204966 title "Algebraic Properties of First Integrals for Scalar Linear Third-Order ODEs of Maximal Symmetry" @default.
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- W2022204966 doi "https://doi.org/10.1155/2013/530365" @default.
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