A simple method to find out when an ordinary differential equation is separable

• Autores: José Ángel Cid Araújo
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 40, Nº. 5, 2009, págs. 659-662
• Idioma: inglés
• DOI: 10.1080/00207390802136578
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• Resumen

  • We present an alternative method to that of Scott (D. Scott, When is an ordinary differential equation separable?, Amer. Math. Monthly 92 (1985), pp. 422-423) to teach the students how to discover whether a differential equation [image omitted] is separable or not when the nonlinearity f(x, y) is not explicitly factorized. Our approach is completely elementary and provides a necessary and sufficient condition for separability, as well as simple formulas for the explicit factors of f(x, y).