Answer: In Exercises 7 and 8, make a change of variable
Chapter 5, Problem 7E(choose chapter or problem)
Problem 7E
In Exercises 7 and 8, make a change of variable that decouples the equation x’ = Ax. Write the equation x (t) = Py(t) and show the calculation that leads to the uncoupled system y’ = Dy, specifying P and D.
A as in Exercise 5
Reference:
In Exercises 3–6, solve the initial value problem x’(t) = Ax(t) for. Classify the nature of the origin as an attractor, repeller, or saddle point of the dynamical system described by x’ = Ax.Find the directions of greatest attraction and/or repulsion. When the origin is a saddle point, sketch typical trajectories.
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