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Abstract <p>The article is devoted to ordinary differential equations of the second order, the left side of which is the second derivative, and the right side is a third-degree polynomial of the first derivative of the desired function. The algebra of all differential invariants of point transformations is constructed for these equations in the general position, and the equivalence problem is solved for them.</p>

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Differential Invariants and Equivalence of Second Order ODEs

  • 期刊论文

  • 发表日期：

    2025年11月1日

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  • V. A. Yumaguzhin

摘要

Abstract

The article is devoted to ordinary differential equations of the second order, the left side of which is the second derivative, and the right side is a third-degree polynomial of the first derivative of the desired function. The algebra of all differential invariants of point transformations is constructed for these equations in the general position, and the equivalence problem is solved for them.