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Consider the differential equation If y(0) dy dt Use a phase-line analysis to find the long-term behavior of y(t) for each of the following given initial conditions. If the answer is infinite, enter oo for or -oo for -∞. = = If y(0) 8y-2y². -1, then as t increases y(t) approaches If y(0) = 0, then as t increases y(t) approaches If y(0) = 2, then as t increases y(t) approaches = =4, then as t increases y(t) approaches If y(0) = 6, then as t increases y(t) approaches

Consider the differential equation If y(0) dy dt Use a phase-line analysis to find the long-term behavior of y(t) for each of the following given initial conditions. If the answer is infinite, enter oo for or -oo for -∞. = = If y(0) 8y-2y². -1, then as t increases y(t) approaches If y(0) = 0, then as t increases y(t) approaches If y(0) = 2, then as t increases y(t) approaches = =4, then as t increases y(t) approaches If y(0) = 6, then as t increases y(t) approaches

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the differential equation = 8y - 2y². dy dt Use a phase-line analysis to find the long-term behavior of y(t) for each of the following given initial conditions. If the answer is infinite, enter oo for or -oo for -∞. If y(0) = −1, then as t increases y(t) approaches If y(0) = 0, then as t increases y(t) approaches If y(0) = 2, then as t increases y(t) approaches If y(0) = 4, then as t increases y(t) approaches If y(0) = 6, then as t increases y(t) approaches
Transcribed Image Text:Consider the differential equation = 8y - 2y². dy dt Use a phase-line analysis to find the long-term behavior of y(t) for each of the following given initial conditions. If the answer is infinite, enter oo for or -oo for -∞. If y(0) = −1, then as t increases y(t) approaches If y(0) = 0, then as t increases y(t) approaches If y(0) = 2, then as t increases y(t) approaches If y(0) = 4, then as t increases y(t) approaches If y(0) = 6, then as t increases y(t) approaches
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