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Consider the differential equation dy = y²(a - y²) f(a,y) for the values a = -1 and a = 1 and determine their critical points. Plot for each of these differential equations their direction field in the rectangle -2 < t < 10,-2

Consider the differential equation dy = y²(a - y²) f(a,y) for the values a = -1 and a = 1 and determine their critical points. Plot for each of these differential equations their direction field in the rectangle -2 < t < 10,-2

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 15E: Find the general solution for each differential equation. Verify that each solution satisfies the...
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Consider the differential equation dy = y²(a - y²) dt f(a,y) for the values a = -1 and a = 1 and determine their critical points. Plot for each of these differential equations their direction field in the rectangle -2 < t < 10,-2 <y < 2 and the corresponding phase diagram -1.5 < y < 1.5, -20 < f(a,y)< 20. Use these plots to determine whether the critical points are asymptotically stable or unstable.
Transcribed Image Text:Consider the differential equation dy = y²(a - y²) dt f(a,y) for the values a = -1 and a = 1 and determine their critical points. Plot for each of these differential equations their direction field in the rectangle -2 < t < 10,-2 <y < 2 and the corresponding phase diagram -1.5 < y < 1.5, -20 < f(a,y)< 20. Use these plots to determine whether the critical points are asymptotically stable or unstable.
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