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305_pdfsam_math 54 differential equation solutions odd

# 305_pdfsam_math 54 differential equation solutions odd -...

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Exercises 5.4 figure indicates that (0 , 0) is a stable critical point (center) whereas (1 , 0) is a saddle point (unstable). 25. This system has two critical points, (0 , 0) and (1 , 0), which are solutions to the system y = 0 , x + x 3 = 0 . The direction field for this system is depicted in Figure B.37. From this figure we conclude that (a) the solution passing through the point (0 . 25 , 0 . 25) ﬂows around (0 , 0) and thus is periodic; (b) for the solution ( x ( t ) , y ( t )) passing through the point (2 , 2), y ( t ) → ∞ as t → ∞ , and so this solution is not periodic; (c) the solution passing through the critical point (1 , 0) is a constant (equilibrium) solution and so is periodic. 27. The direction field for given system is shown in Figure B.38 in the answers of the text. From the starting point, (1
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