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Consider the differential equation dy dt = 12y - 3y². Draw a phase portrait and sketch typical solution curves. Use your solution curves to find the long- term behavior of y(t) for each of the following given initial conditions. If the answer is infinite, enter ∞ or -∞ as appropriate. If y(0) = -1, then as t increases y(t) approaches If y(0) : = 0, then as t increases y(t) approaches 0 If y(0) = 2, then as t increases y(t) approaches 4 If y(0) = 4, then as t increases y(t) approaches 4 If y(0) = 6, then as t increases y(t) approaches ·∞

Consider the differential equation dy dt = 12y - 3y². Draw a phase portrait and sketch typical solution curves. Use your solution curves to find the long- term behavior of y(t) for each of the following given initial conditions. If the answer is infinite, enter ∞ or -∞ as appropriate. If y(0) = -1, then as t increases y(t) approaches If y(0) : = 0, then as t increases y(t) approaches 0 If y(0) = 2, then as t increases y(t) approaches 4 If y(0) = 4, then as t increases y(t) approaches 4 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 If y(0) dy dt = - Draw a phase portrait and sketch typical solution curves. Use your solution curves to find the long- term behavior of y(t) for each of the following given initial conditions. If the answer is infinite, enter ∞ or -∞ as appropriate. 12y - 3y². -1, then as t increases y(t) approaches -8 If y(0) = 0, then as t increases y(t) approaches 0 If y(0) = 2, then as t increases y(t) approaches 4 If y(0) = 4, then as t increases y(t) approaches 4 If y(0) = 6, then as t increases y(t) approaches
Transcribed Image Text:Consider the differential equation If y(0) dy dt = - Draw a phase portrait and sketch typical solution curves. Use your solution curves to find the long- term behavior of y(t) for each of the following given initial conditions. If the answer is infinite, enter ∞ or -∞ as appropriate. 12y - 3y². -1, then as t increases y(t) approaches -8 If y(0) = 0, then as t increases y(t) approaches 0 If y(0) = 2, then as t increases y(t) approaches 4 If y(0) = 4, then as t increases y(t) approaches 4 If y(0) = 6, then as t increases y(t) approaches
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