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2:52
YouTube
MathSci Consult
How to Solve Exact Differential Equations
In this video, you will learn how to solve exact differential equations step by step, using a clear and structured approach with worked examples. We explain: - What an exact differential equation is - How to test whether a differential equation is exact - How to integrate exact equations with respect to x and y - How to find the missing ...
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We simulate the advection of a passive scalar by a simple rotation flow u, generating a converging spiral. In particular, we use a simple flow with |u|~r², such that angular velocity increases linearly with the distance to the center. The solution is exact, calculated by differential rotation of the initial condition by |u(r)|/r for each radius r. Rotation speed is chosen such that a complete outer rotation is achieved at t=1. #physics #mathematics #differentialequations #calculus #visualization
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