Draw a direction field and plot (or sketch) several solutions of the differential equation y' = -y(6 - ty). Describe how solutions appear to behave as t increases and how their behavior depends on the initial value Yo when t = 0. For yo36 the solutions tend to zero, and for yo> 36 the solutions

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 77E
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Draw a direction field and plot (or sketch) several solutions of the
differential equation y'= -y(6 - ty). Describe how solutions appear
to behave as t increases and how their behavior depends on the initial
value yo when t = 0.
For yo 36
the solutions tend to zero,
and for yo> 36 the solutions
Choose one
tend to zero as well.
tend to infinity.
oscillate about an average of 6².
tend to 6².
Transcribed Image Text:Draw a direction field and plot (or sketch) several solutions of the differential equation y'= -y(6 - ty). Describe how solutions appear to behave as t increases and how their behavior depends on the initial value yo when t = 0. For yo 36 the solutions tend to zero, and for yo> 36 the solutions Choose one tend to zero as well. tend to infinity. oscillate about an average of 6². tend to 6².
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