{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

nagle_differential_equations_ISM_Part38

# nagle_differential_equations_ISM_Part38 - Exercises 5.4 for...

This preview shows pages 1–3. Sign up to view the full content.

Exercises 5.4 for y < 0, | x | > 1, y = - c x 2 - 1; for y < 0, | x | < 1, y = - c 1 - x 2 ; all with c 0 If c = 1, y = ± 1 - x 2 are semicircles ending at (1 , 0) and ( - 1 , 0) 12. 9 x 2 + 4 y 2 = c . See Fig. 5–B on page 187 14. y = cx 2 / 3 See Fig. 5–C on page 187 16. (0 , 0) is a stable node. See Fig. 5–D on page 188 18. (0 , 0) is an unstable node; (0 , 5) is a stable node; (7 , 0) is a stable node; (3 , 2) is a saddle point; See Fig. 5–E on page 188 20. y = v v = - y (0 , 0) is a center. See Fig. 5–F on page 189 22. y = v v = - y 3 (0 , 0) is a center. See Fig. 5–G on page 189 24. y = v v = - y + y 3 (0 , 0) is a center; ( - 1 , 0) is a saddle point; (1 , 0) is a saddle point. See Fig. 5–H on page 190 26. x 2 2 + x 4 4 + y 2 2 = c ; all solutions are bounded. See Fig. 5–I on page 190 28. (0 , 0) is a center; (1 , 0) is a saddle point 30. (a) x x * , y y * , f and g are continuous implies x ( t ) f ( x ( t ) , y ( t )) f ( x * , y * ) and y ( t ) g ( x ( t ) , y ( t )) g ( x , y * ) (b) x ( t ) = t T x ( τ ) + t ( T ) > f ( x * , y * ) 2 ( t - T ) + x ( T ) f ( x * , y * ) t 2 + C 181

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Chapter 5 (c) If f ( x * , y * ) > 0, f ( x * , y * ) t → ∞ implying x ( t ) → ∞ (d) Similar (e) Similar 32.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 5

nagle_differential_equations_ISM_Part38 - Exercises 5.4 for...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online