Variation of Parameters in Differential Equations (A Variation in Making Sense of Variation of Parameters)

• Autores: Terry Quinn, Sanjay Rai
• Localización: Primus: problems, resources, and issues in mathematics undergraduate studies, ISSN 1051-1970, Vol. 23, Nº. 1, 2012-2013, págs. 25-44
• Idioma: inglés
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• Resumen

  • The method of variation of parameters can be found in most undergraduate textbooks on differential equations. The method leads to solutions of the non-homogeneous equation of the form Y = U1 Y1 + U2 Y2, a sum of function products using solutions to the homogeneous equation U1 and Y2. Why though, might varying parameters of solutions to the homogeneous equation be a feasible approach? An insight is needed, even for a good guess. This paper is for instructors teaching a first course in undergraduate differential questions, where the students already have covered first-order linear equations and second-order homogeneous linear equations. We provide a variation to the standard textbook approach to variation of parameters, intended to help the student find their way toward a key insight: �Aha! Let's try �� We point to several reasons why it can be important for students to learn variation of parameters.