The discussion focuses on the simplification of the differential equation \(\frac{2e^{t}+C}{e^{t}} = 2e^{-t} + C\). The user expresses confusion regarding the transformation to \(e^{-t}\) and questions the steps leading to the final result. The correct simplification involves recognizing that \(\frac{e^{t}}{e^{t}} = 1\) and applying the property of exponents, leading to the conclusion that \(C e^{-t}\) is the appropriate form. The user mistakenly equates \(e^{-t}\) to \(-1\), which is incorrect.
PREREQUISITESStudents and professionals in mathematics, particularly those studying differential equations, as well as educators looking to clarify concepts related to exponential functions and algebraic simplification.