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Using Theorem 7.5.2, show that the linear autonomous sys

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Using Theorem 7.5.2, show that the linear autonomous system dx dt = a11x + a12y, dy dt = a21x + a22y does not have a per

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Using Theorem 7.5.2, show that the linear autonomous system dx dt = a11x + a12y, dy dt = a21x + a22y does not have a periodic solution (other than x = 0, y = 0) if a11 + a22 ? 0. In each of Problems 11 and 12, show that the given system has no periodic solutions other than constant solutions:

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