Differential Equations › Section E · Systems of differential equations › Topic E.5
Real eigenvalues
When the matrix of a system has two different real eigenvalues, the general solution is just two exponentials, each riding along its own eigenvector. This topic solves such systems, fits initial conditions, and turns the formulas into phase portraits of saddles and nodes.
In this topic
- Two eigenvalues, two solutions
- The method
- Worked example: a saddle
- The saddle's phase portrait
- Worked example: salt in two tanks
- Reading the tank solution
- The node's phase portrait
- Larger systems and component form
- Common mistakes to avoid
- Key takeaways
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