1. Eigenvalues: $-2,-3$; stable node

2. Eigenvalues: 1, 3; unstable node

3. Eigenvalues: $-3,$ 5; unstable saddle point

4. Eigenvalues: $-1\pm 2i$; stable spiral point

5. Critical points: $(0,n\pi )$ where n is an integer; an unstable saddle point if n is even, a stable spiral point if n is odd

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: $(n\pi ,n\pi )$ where n is an integer; an unstable saddle point if n is even, a stable spiral point if n is odd

8. Critical points: $(n\pi ,0)$ 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 $(n\pi ,0)$ is an unstable saddle point.

10. If n is odd then $(n\pi ,0)$ is a stable node.

11. $(n\pi ,0)$ 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.

18. (0, 0) is a spiral sink; the points $(\pm 2,0)$ are saddle points.

19. (0, 0) is a spiral sink.

20. $(n\pi ,0)$ is a spiral sink if n is even, a saddle point if n is odd.