Differential invariants and equivalence of ODEs $y''=a^3(x,y)y'^3+a^2(x,y)y'^2+a^1(x,y)y'+a^0(x,y)$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912565786836992 |
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| author | Yumaguzhin, Valeriy A. |
| author_facet | Yumaguzhin, Valeriy A. |
| contents | This paper is devoted to ordinary differential equations of the form $$y''=a^3(x,y)y'^3+a^2(x,y)y'^2+a^1(x,y)y'+a^0(x,y)$$ The algebra of all differential invariants of point transformations is constructed for these equations in general position and the equivalence problem is solved for them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_21439 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Differential invariants and equivalence of ODEs $y''=a^3(x,y)y'^3+a^2(x,y)y'^2+a^1(x,y)y'+a^0(x,y)$ Yumaguzhin, Valeriy A. Differential Geometry Classical Analysis and ODEs This paper is devoted to ordinary differential equations of the form $$y''=a^3(x,y)y'^3+a^2(x,y)y'^2+a^1(x,y)y'+a^0(x,y)$$ The algebra of all differential invariants of point transformations is constructed for these equations in general position and the equivalence problem is solved for them. |
| title | Differential invariants and equivalence of ODEs $y''=a^3(x,y)y'^3+a^2(x,y)y'^2+a^1(x,y)y'+a^0(x,y)$ |
| topic | Differential Geometry Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2508.21439 |