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Differential Equations Application Example: Mixing Problem

In this example problem video, we solve a mixing problem using differential equations. We model how the amount of salt in a tank changes over time by setting up a rate equation that accounts for salt flowing into and out of the tank. The resulting differential equation is separable and can be solved explicitly to find the amount of salt as a function of time. In this video, you’ll see examples involving: • Setting up a mixing problem using rate in minus rate out • Writing a differential equation for the amount of salt • Solving a separable differential equation • Applying an initial condition • Finding the amount of salt at a given time These worked examples show how differential equations are used to model real-world mixing processes. This video is part of my Differential Equations application examples series. Differential Equations playlists:    / @understandthemath   Guided notes and additional resources: https://www.understandthemath.com ODE Videos    • Ordinary Differential Equations Free Cours...      • Classification of Differential Equations |...      • Slope Fields for First-Order Differential ...      • Autonomous Differential Equations | Critic...      • Separable Differential Equations | Definit...      • Linear Differential Equations | Integratin...      • Exact Differential Equations | Definition,...      • Homogeneous Differential Equations | Defin...      • Bernoulli Differential Equations | Method,...      • Applications of First-Order Linear Differe...      • Euler’s Method | Numerical Approximation f...      • Differential Equations Midterm Exam Review...   Connect & Support TikTok:   / understandthemath   Instagram:   / understandthemath   Facebook: https://www.facebook.com/profile.php?... Support: https://buymeacoffee.com/understandth... More About Understand The Math Understand The Math offers clear, accessible, and engaging mathematics instruction for students and lifelong learners. I'm Cheryl Hile, the founder of Understand The Math, with a Ph.D. in Engineering Science and Applied Mathematics and over 25 years of university teaching experience. My goal is to provide accurate, high-quality math instruction through step-by-step explanations and carefully worked-out examples. Each video includes free guided notes, linked in the description. These notes help students follow along, highlight key concepts, and practice problems, making review easier and more effective. #DifferentialEquations #MixingProblem #ApplicationsOfDifferentialEquations #ODEs #MathExamples #EngineeringMath #AppliedMath #CollegeMath #UnderstandTheMath