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<p>Our aim is to revisit the fundamental theorem of higher-order homogeneous linear differential equations with constant coefficients in an elementary and direct manner. The approach is based on a recursive factorization of the attached differential operator and it is motivated by a comment of Euler. We use elementary arguments, like the Viéte formulae and the fundamental theorem of calculus, and also discuss, how this method applies to the nonhomogeneous case.</p>

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De integratione aequationum: an idea of Euler elaborated

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月29日

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  • Mihály Bessenyei,
  • Tímea Kamilla Makai

摘要

Our aim is to revisit the fundamental theorem of higher-order homogeneous linear differential equations with constant coefficients in an elementary and direct manner. The approach is based on a recursive factorization of the attached differential operator and it is motivated by a comment of Euler. We use elementary arguments, like the Viéte formulae and the fundamental theorem of calculus, and also discuss, how this method applies to the nonhomogeneous case.