MathPlotAI Logo MathPlotAI

Slope field of a differential equation

Slope field of a differential equation
Loading the math board and drawing, please wait…
2020-01-12 02:07
VectorFunctionCoordinate GeometryCalculusDerivative
This example demonstrates the slope field of a differential equation, visually showing the direction of solution curves. Key math concepts include differential equations, slope fields, numerical integration, derivatives, and coordinate geometry. Construction highlights involve commands/objects like SlopeField, Textfield, SolveODE, Vector, UnitVector, ImplicitCurve. Suitable for university students in mathematics, physics, etc., studying differential equations.

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