1. Eigenvalues: −2, −3; stable node
![](http://imgdetail.ebookreading.net/202009/01/9780136739692/9780136739692__differential-equations-and__9780136739692__images__FigA9.4.1.png)
2. Eigenvalues: 1, 3; unstable node
3. Eigenvalues: −3, 5; unstable saddle point
![](http://imgdetail.ebookreading.net/202009/01/9780136739692/9780136739692__differential-equations-and__9780136739692__images__FigA9.4.3.png)
4. Eigenvalues: −1±2i; stable spiral point
![](http://imgdetail.ebookreading.net/202009/01/9780136739692/9780136739692__differential-equations-and__9780136739692__images__FigA9.4.4.png)
5. Critical points: (0, nπ) where n is an integer; an unstable saddle point if n is even, a stable spiral point if n is odd
![](http://imgdetail.ebookreading.net/202009/01/9780136739692/9780136739692__differential-equations-and__9780136739692__images__FigA9.4.5.png)
6. Critical points: (n, 0) where n is an integer; an unstable saddle point if n is even, a stable spiral point if n is odd
7. Critical points: (nπ, nπ) where n is an integer; an unstable saddle point if n is even, a stable spiral point if n is odd
![](http://imgdetail.ebookreading.net/202009/01/9780136739692/9780136739692__differential-equations-and__9780136739692__images__FigA9.4.7.png)
8. Critical points: (nπ, 0) where n is an integer; an unstable nodeif n is even, an unstable saddle point if n is odd
9. If n is odd then (nπ, 0) is an unstable saddle point.
10. If n is odd then (nπ, 0) is a stable node.
11. (nπ, 0) is a stable spiral point.
12. Unstable saddle points at (2, 0) and (−2, 0), a stable center at (0, 0)
13. Unstable saddle points at (2, 0) and (−2, 0), a stable spiral point at (0, 0)
14. Stable centers at (2, 0) and (−2, 0), an unstable saddle point at (0, 0)
15. A stable center at (0, 0) and an unstable saddle point at (4, 0)
16. Stable centers at (2, 0), (0, 0) and (−2, 0), unstable saddle points at (1, 0) and (−1, 0)
17. (0, 0) is a spiral sink.
![](http://imgdetail.ebookreading.net/202009/01/9780136739692/9780136739692__differential-equations-and__9780136739692__images__FigA9.4.17.png)
18. (0, 0) is a spiral sink; the points (±2, 0) are saddle points.
![](http://imgdetail.ebookreading.net/202009/01/9780136739692/9780136739692__differential-equations-and__9780136739692__images__FigA9.4.18.png)
19. (0, 0) is a spiral sink.
![](http://imgdetail.ebookreading.net/202009/01/9780136739692/9780136739692__differential-equations-and__9780136739692__images__FigA9.4.19.png)
20. (nπ, 0) is a spiral sink if n is even, a saddle point if n is odd.