When the eigenvalues of the coefficient matrix are complex, the origin is a spiral. If

Chapter 10, Problem 30

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When the eigenvalues of the coefficient matrix are complex, the origin is a spiral. If the eigenvalues are purely imaginary (that is, the real parts are zero), then the origin is called a center. For example, this is true of the following system: dx dt c 21 2 23 1d x Theorem 2 still applies to this system, and we can obtain the general solution (13) in the usual way. (a) Find the general solution. (b) Use the general solution in part (a) to prove that the solutions form closed curves in the phase plane.

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