隐微分方程示例：几何与三角函数的综合应用

GeoGebra 命令及参数

1. Vector((a, 0)) → u
2. Vector((a, 0), (a, b)) → v
3. Vector((0, 0), (a, b)) → w
4. Vector((0, 0), (a, c)) → d
5. Vector((a, 0), (a, c)) → e
6. Vector((o, 0)) → s
7. Vector((0, o)) → u_1
8. Vector((o, 0), (0, o)) → v_1
9. Point(u_1) → A
10. Point(s) → B
11. Polygon(C, B, A) → poly1, a_2, c_1, b_2
12. Rotate(h_4, -80*°, C) → e_1
13. Point(e_1) → D
14. Point(e_1) → E
15. Polygon(C, E, D) → poly2, d_2, c_2, e_2
16. Segment(C, D) → g_1
17. Segment(C, E) → i_1
18. Angle(E, C, D) → α_i
19. Point(d) → F
20. Point(u) → G
21. Circle(C, F) → p_1
22. Circle(C, A) → q_1
23. Point(u) → H
24. Circle(C, H) → r_1
25. Circle(C, z_1) → s_1
26. Circle(C, z_2) → t_1
27. Circle(C, z_3) → f_2
28. Circle(C, z_4) → g_2
29. Circle(C, z_5) → h_2
30. Distance(C, z_1) → distanceCz1
31. Distance(C, z_2) → distanceCz2
32. Distance(C, z_3) → distanceCz3
33. Distance(C, z_4) → distanceCz4
34. Distance(C, z_5) → distanceCz5
35. Line(I, v_1) → a_3
36. Mirror(C, a_3) → C'
37. Mirror(B, a_3) → B'
38. Mirror(A, a_3) → A'
39. Mirror(C, a_3) → C'_1
40. Mirror(B, a_3) → B'_1
41. Mirror(A, a_3) → A'_1
42. Polygon(C'_1, B'_1, A'_1) → poly1', a'_1, c'_1, b'_1
43. Point(c_1) → J
44. Point(c'_1) → K
45. Point(a_2) → L
46. Point(a'_1) → M
47. Vector(K, J) → w_2
48. Vector(M, L) → u_3
49. Mirror(d, a_2) → d'
50. Mirror(w, a_2) → w'
51. Mirror(v, a_2) → v'
52. Mirror(e, a_2) → e'
53. Distance(K, J) → distanceKJ
54. Distance(K, M) → distanceKM
55. Mirror(v_1, xAxis) → v_3
56. Mirror(u_1, xAxis) → w_3
57. Point(s) → N
58. Point(u_1) → O
59. Circle(N, O) → d_3
60. Circle(A, x_7) → k_3
61. Circle(A, x_6) → p_3
62. Segment(P, Q) → j_3