Calculus 2, Lecture 9A, Logistic Model, Separation of Variables, Partial Fractions

Calculus 2, Lecture 9A.

(0:00) Reminder about the Gateway Exam.
(0:43) Topics for the lectures.
(1:32) Differential equations, Example 1: dy/dx = sin(x) + x^2, y(0) = 4.
(4:58) Example 2: dy/dx = 3y, y(0) = 5 (solve first by guessing and then use separation of variables).
(11:52) Mention that example 2 has applications to exponential growth (it also has applications to exponential decay).
(12:54) Example 3: Logistic growth model applied to a rabbit population.
(18:09) Solve the differential equation by separation of variables and the use of the method of partial fractions.