Chapter 17 · Ordinary Differential Equations
17.10
Systems of Differential Equations
Several interacting quantities give a system x' = Ax. Eigenvalues and eigenvectors of A give the solutions, and their signs decide the picture: saddle, node, spiral or center.
About 17 minutes
You'll learn to
- →Write higher-order equations as first-order systems
- →Find eigenvalues and eigenvectors of a 2×2 matrix
- →Solve x' = Ax with real distinct eigenvalues
- →Classify the phase portrait from the eigenvalues