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Phase Plane System of Differential Equations

Phase Plane System of Differential Equations
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2020-03-24 21:00
VectorFunctionCalculusOptimizationParametric Equation
This example demonstrates the trajectories and vector field of a system of differential equations in the phase plane using GeoGebra. Key mathematical concepts include differential equations, phase plane analysis, vector fields, and isoclines. Construction highlights the use of commands like SlopeField, Textfield, SolveODE, Vector, UnitVector, and ImplicitCurve. Suitable for university students in mathematics, physics, or engineering to understand dynamical systems and stability analysis.

GeoGebra Commands & Parameters

  1. SlopeField(v(x, y) / u(x, y), N, l, xmin, ymin, xmax, ymax) → slopefield1
  2. Textfield(u) → InputBox1
  3. Textfield(v) → InputBox2
  4. SolveODE(v(x, y) / u(x, y), x(A), y(A), tmin, numStep) → fAback
  5. SolveODE(v(x, y) / u(x, y), x(A), y(A), tmax, numStep) → fAforw
  6. SolveODE(v(x, y) / u(x, y), x(B), y(B), tmin, numStep) → fBback
  7. SolveODE(v(x, y) / u(x, y), x(B), y(B), tmax, numStep) → fBforw
  8. Vector((u(x(B), y(B)), v(x(B), y(B)))) → VB
  9. UnitVector(VA) → vA
  10. UnitVector(VB) → vB
  11. Vector(A, A + vA) → v_A
  12. Vector(B, B + vB) → v_B
  13. ImplicitCurve(u(x, y)) → IsoclineX
  14. ImplicitCurve(v(x, y)) → IsoclineY
  15. Textfield(numStep) → InputBox3
  16. Textfield(tmax) → InputBox4

AI Drawing Prompt Reference

Draw the trajectories and vector field of a differential equation system on a plane, showing vector directions and isoclines, marking integral curves starting from two fixed points with different colors, indicating directions with unit vectors, and adding text boxes for the equations and step parameters.
The prompt above was compiled from the original drawing commands and is for reference only.