Slope Fields: Example 2

Example: Consider the autonomous differential equation with the initial condition

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where the graph of f(y) is given below


1.
Draw the phase line for this differential equation, and classify the equilibrium points (critical points) as sinks, sources, or nodes.
2.
Give a rough sketch of the slope field for this differential equation, and draw a few solutions into the slope field.
3.
Consider the solution to the differential equation which satisfies the initial condition y(1)=2. Find

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4.
Same as in 3., if y(2)=1, that is find

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Solution.

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Author: Helmut Knaust
Last Update 6-22-98

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