A portion of the direction field for the differential equation 17 1 1 /// // 1 dy dt = f(y) is shown below: 1/8 /// The dotted horizontal line has equation y = 9. Fill in the following chart to indicate the behavior as t→ ∞ of the solution y(t) of the differential equation corresponding to each initial condition yo.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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A portion of the direction field for the differential equation
18
4.5
0
dy
dt
The dotted horizontal line has equation y = 9. Fill in the following chart to indicate the behavior as t→ ∞o of the solution y (t) of the
differential equation corresponding to each initial condition yo.
Initial Condition yo Behavior of y(t) ast → ∞
9
= f (y) is shown below:
✓ Y
/ / / / / / / /
////
111 11 1
/ / / X / / / /
1118 1
Approaches the line y = 9
Approaches the x-axis
Tends toward -∞
Tends toward ∞
4 options
Transcribed Image Text:A portion of the direction field for the differential equation 18 4.5 0 dy dt The dotted horizontal line has equation y = 9. Fill in the following chart to indicate the behavior as t→ ∞o of the solution y (t) of the differential equation corresponding to each initial condition yo. Initial Condition yo Behavior of y(t) ast → ∞ 9 = f (y) is shown below: ✓ Y / / / / / / / / //// 111 11 1 / / / X / / / / 1118 1 Approaches the line y = 9 Approaches the x-axis Tends toward -∞ Tends toward ∞ 4 options
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