Show that (0, 0) is an unstable critical point for the following system: 2xy + x3, 1 -x2 + y°. de dy dt

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.CR: Chapter 11 Review
Problem 12CR
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Do question number 8th as soon as possible
8. Show that (0,0) is an unstable critical point for the following system:
2xy + x³, ]
= -x2 + y°.
}
dr
dt
dt
9. The one-dimensional heat conduction equation for a thin rod of length L is given by
u" = - f(x) and assume that the ends of the rod at x = 0 and x = L are maintained at
zero degree temperature. By utilizing the properties of Green's function, construct the
Green's function for this boundary value problem.
Transcribed Image Text:8. Show that (0,0) is an unstable critical point for the following system: 2xy + x³, ] = -x2 + y°. } dr dt dt 9. The one-dimensional heat conduction equation for a thin rod of length L is given by u" = - f(x) and assume that the ends of the rod at x = 0 and x = L are maintained at zero degree temperature. By utilizing the properties of Green's function, construct the Green's function for this boundary value problem.
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