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System of Linear DEs Real Distinct Eigenvalues #1

System of Linear DEs Real Distinct Eigenvalues #1
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2016-01-01 23:41
VectorFunctionCalculusComplex NumberGeometric Construction
In collections Differential Equations
This example demonstrates the phase portrait for a linear system of differential equations with constant coefficients and two real, distinct eigenvalues. Key math concepts include systems of linear differential equations, eigenvalues, phase plane, vector field. Construction highlights use of GeoGebra commands/objects like SolveODE, Intersect, Line. Suitable for university mathematics courses or differential equations learning.

GeoGebra Commands & Parameters

  1. SolveODE(g, f, x(A), y(A), 10, 0.001) → numericalIntegral1
  2. SolveODE(g, f, x(D), y(D), 10, 0.001) → numericalIntegral2
  3. SolveODE(g, f, x(E), y(E), 10, 0.001) → numericalIntegral3
  4. SolveODE(g, f, x(B), y(B), 10, 0.001) → numericalIntegral4
  5. SolveODE(g, f, x(C), y(C), 10, 0.001) → numericalIntegral5
  6. SolveODE(g, f, x(G), y(G), 10, 0.001) → numericalIntegral7
  7. SolveODE(g, f, x(H), y(H), 10, 0.001) → numericalIntegral6
  8. SolveODE(g, f, x(F), y(F), 10, 0.001) → numericalIntegral8
  9. Intersect(xAxis, yAxis) → K
  10. Line(K, J) → a
  11. Line(K, I) → b