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常微分方程解曲线的动态展示

常微分方程解曲线的动态展示
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2019-09-08 11:52
微积分函数图像
这个范例展示了常微分方程解曲线的动态变化。它涉及的核心数学概念包括常微分方程、解曲线、斜率场等。通过使用SolveODE和SlopeField命令，用户可以观察到解曲线随参数变化的动态效果。适合高中及以上学生或教师使用，用于教学或研究。

GeoGebra 命令及参数

  1. SolveODE(f(x, y), Ax, Ay, 100, 0.08) → sol
  2. SlopeField(f) → slp
  3. SolveODE(f(x, y), Ax, Ay + 0 - 0.8, 100, 0.08) → A1
  4. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (2 - 1)) - 0.8, 100, 0.08) → A2
  5. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (3 - 1)) - 0.8, 100, 0.08) → A3
  6. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (4 - 1)) - 0.8, 100, 0.08) → A4
  7. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (5 - 1)) - 0.8, 100, 0.08) → A5
  8. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (6 - 1)) - 0.8, 100, 0.08) → A6
  9. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (7 - 1)) - 0.8, 100, 0.08) → A7
  10. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (8 - 1)) - 0.8, 100, 0.08) → A8
  11. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (9 - 1)) - 0.8, 100, 0.08) → A9
  12. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (10 - 1)) - 0.8, 100, 0.08) → A10
  13. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (11 - 1)) - 0.8, 100, 0.08) → A11
  14. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (12 - 1)) - 0.8, 100, 0.08) → A12
  15. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (13 - 1)) - 0.8, 100, 0.08) → A13
  16. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (14 - 1)) - 0.8, 100, 0.08) → A14
  17. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (15 - 1)) - 0.8, 100, 0.08) → A15
  18. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (16 - 1)) - 0.8, 100, 0.08) → A16
  19. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (17 - 1)) - 0.8, 100, 0.08) → A17
  20. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (18 - 1)) - 0.8, 100, 0.08) → A18
  21. SolveODE(f(x, y), Ax, Ay + 0 - 0.8, -100, 0.08) → B1
  22. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (2 - 1)) - 0.8, -100, 0.08) → B2
  23. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (3 - 1)) - 0.8, -100, 0.08) → B3
  24. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (4 - 1)) - 0.8, -100, 0.08) → B4
  25. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (5 - 1)) - 0.8, -100, 0.08) → B5
  26. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (6 - 1)) - 0.8, -100, 0.08) → B6
  27. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (7 - 1)) - 0.8, -100, 0.08) → B7
  28. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (8 - 1)) - 0.8, -100, 0.08) → B8
  29. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (9 - 1)) - 0.8, -100, 0.08) → B9
  30. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (10 - 1)) - 0.8, -100, 0.08) → B10
  31. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (11 - 1)) - 0.8, -100, 0.08) → B11
  32. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (12 - 1)) - 0.8, -100, 0.08) → B12
  33. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (13 - 1)) - 0.8, -100, 0.08) → B13
  34. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (14 - 1)) - 0.8, -100, 0.08) → B14
  35. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (15 - 1)) - 0.8, -100, 0.08) → B15
  36. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (16 - 1)) - 0.8, -100, 0.08) → B16
  37. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (17 - 1)) - 0.8, -100, 0.08) → B17
  38. SolveODE(f(x, y), Ax, Ay + (13 / 170 * (18 - 1)) - 0.8, -100, 0.08) → B18