{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

305_pdfsam_math 54 differential equation solutions odd

305_pdfsam_math 54 differential equation solutions odd -...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}