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System of Linear DEs with Real Repeated Eigenvalues

System of Linear DEs with Real Repeated Eigenvalues
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2016-01-02 00:10
VectorCalculus
In collections Differential Equations
This example demonstrates the phase portrait of a linear system of differential equations with constant coefficients and two real, equal (repeated) eigenvalues. It uses commands like SolveODE, Intersect, and Line to construct the system, suitable for studying linear differential equations and phase portraits.

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. SolveODE(g, f, x(I), y(I), 10, 0.001) → numericalIntegral9
  10. Intersect(xAxis, yAxis) → J
  11. Line(J, K) → a

AI Drawing Prompt Reference

Draw the phase portrait of a linear system of differential equations with two real and equal eigenvalues. First, use the SolveODE command to solve the differential equations and obtain numerical integration results. Then, find the intersection point J of the x-axis and y-axis, and draw a line a connecting point J and K.
The prompt above was compiled from the original drawing commands and is for reference only.