Slope Fields: Example 1

Example: Consider the autonomous differential equation

displaymath32,

where the graph of f(y) is given by


1.
Sketch the Slope Fields of this differential equation.
(Hint: the graph of the solutions and the graph of f(y) are two different entities.)
2.
Sketch the graph of the solution to the IVP

displaymath38

Find the limit displaymath40.

3.
Sketch the graph of the solution to the IVP

displaymath42

Find the limit displaymath40.

Solution.

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Author: Mohamed Amine Khamsi
Last Update 6-22-98

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