Resumen de Variation of Parameters in Differential Equations (A Variation in Making Sense of Variation of Parameters)
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.
