Calc 2, Lec 33A, Differential Equations: Logistic Growth, Free Fall w/ Air Resistance, Slope Fields

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Calculus 2, Lecture 33A. More differential equations examples and solutions.

(0:00) Lecture plan.
(0:47) Logistic model of population growth.
(2:47) Confirm Mathematica output by using the method of separating variables by hand.
(11:24) Finish by solving for the unique solution of arbitrary initial-value problem.
(14:03) Graph solutions in the slope field (use VectorPlot in Mathematica), taking note of equilibrium solutions.
(27:48) Free fall with air resistance proportional to the velocity (with opposite sign).
(33:35) Have Mathematica solve the differential equation with DSolveValue and plot the solution in the slope field.
  1. Bill Kinney
  2. differential equation
  3. ODE
  4. exponential growth
  5. logistic
  6. logistic model
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