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Use the phase-plane method to show that the solution to the nonlinear second-order differential equation x + 6x-x²-0 that satisfies x(0)-1 and x(0)-0 is periodic. Let dx of y. Then the differential equation y X(0) (x(0), x(0)) (1, 0) then the particular solution is corresponding value(s) of y. Therefore X(t) is a periodic solution. can be solved by separating variables. It follows that the general solution is But for each x such that 4-2√6

Use the phase-plane method to show that the solution to the nonlinear second-order differential equation x + 6x-x²-0 that satisfies x(0)-1 and x(0)-0 is periodic. Let dx of y. Then the differential equation y X(0) (x(0), x(0)) (1, 0) then the particular solution is corresponding value(s) of y. Therefore X(t) is a periodic solution. can be solved by separating variables. It follows that the general solution is But for each x such that 4-2√6

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.CR: Chapter 11 Review
Problem 5CR
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Use the phase-plane method to show that the solution to the nonlinear second-order differential equation x + 6x-x²-0 that satisfies x(0)-1 and x(0)-0 is periodic. Let dx of y. Then the differential equation y X(0) (x(0), x(0)) (1, 0) then the particular solution is corresponding value(s) of y. Therefore X(t) is a periodic solution. can be solved by separating variables. It follows that the general solution is But for each x such that 4-2√6<x< 1, the particular solution has x X , and since)
Transcribed Image Text:Use the phase-plane method to show that the solution to the nonlinear second-order differential equation x + 6x-x²-0 that satisfies x(0)-1 and x(0)-0 is periodic. Let dx of y. Then the differential equation y X(0) (x(0), x(0)) (1, 0) then the particular solution is corresponding value(s) of y. Therefore X(t) is a periodic solution. can be solved by separating variables. It follows that the general solution is But for each x such that 4-2√6<x< 1, the particular solution has x X , and since)
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