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System of Linear DEs with Real Distinct Eigenvalues #3

System of Linear DEs with Real Distinct Eigenvalues #3
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2016-01-01 23:53
VectorCalculusMatrix
In collections Differential Equations
This example demonstrates the phase portrait of a linear system of differential equations with two real, distinct eigenvalues, where the eigenvalues form a stable node. Key mathematical concepts include linear differential equations, eigenvalues, and eigenvectors. The example uses the SolveODE command to solve the differential equations and constructs the phase portrait. Suitable for university-level calculus and linear algebra courses.

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