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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

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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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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