Solving mixture problems in applied mathematics: a differential equation approach

This study explores the dynamic behavior of solute concentration in a tank system subjected to continuous inflow and outflow of a salt solution. By applying first-order linear differential equations. It reveals how the solute concentration evolves over time, transitioning from an initial state of pure water to a steady-state equilibrium. The findings highlight the critical role of parameters such as inflow rate and concentration in determining the system's long-term behavior. This analysis provides valuable insights into the mechanisms governing mixture processes, offering practical implications for fields like chemical engineering and environmental science, where precise control of concentration dynamics is essential for optimizing operational efficiency and safety.