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Dancing Solution Curves of ODEs by Juan Carlos Ponce Campuzano

Dancing Solution Curves of ODEs by Juan Carlos Ponce Campuzano
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2019-09-08 11:52
CalculusGraphing
This example demonstrates the dynamic changes of solution curves of ordinary differential equations. It involves core mathematical concepts such as ordinary differential equations, solution curves, and slope fields. By using the SolveODE and SlopeField commands, users can observe the dynamic effects of solution curves changing with parameters. Suitable for high school and above students or teachers for teaching or research.

GeoGebra Commands & Parameters

  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