Solving ay´´ + by' + cy = 0 with a simple product rule approach.

• Autores: John Tolle
• Localización: Primus: problems, resources, and issues in mathematics undergraduate studies, ISSN 1051-1970, Vol. 21, Nº. 2, 2011 (Ejemplar dedicado a: A Tribute to Brian J. Winkel), págs. 183-188
• Idioma: inglés
• DOI: 10.1080/10511970903334352
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• Resumen

  • When elementary ordinary differential equations (ODEs) of first and second order are included in the calculus curriculum, second-order linear constant coefficient ODEs are typically solved by a method more appropriate to differential equations courses. This method involves the characteristic equation and its roots, complex-valued solutions, and some method (often mysterious, unnatural, or simply left unjustified) for establishing te rt as a solution when r is the only real root. Here we outline a seldom used but more natural approach better suited to the calculus curriculum. Complex numbers are not needed, and the solution te rt arises constructively.