Differential Equations › Section E · Systems of differential equations › Topic E.7
Repeated eigenvalues
When the two eigenvalues of a 2 × 2 matrix coincide, there may be only one eigenvector, and the method of the last two topics runs one solution short. A generalised eigenvector supplies the missing solution and explains the bent trajectories of a degenerate node.
In this topic
- When the roots coincide
- The easy case: A = λI
- Why t times the first solution fails
- The second solution
- Worked example: an unstable degenerate node
- Choosing w
- The degenerate node
- Worked example: a stable degenerate node
- Links and larger systems
- Common mistakes to avoid
- Key takeaways
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