Differential Equations Quiz
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SYSTEMS OF DIFFERENTIAL EQUATIONS
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A system x′=Ax\mathbf{x}' = A\mathbf{x} has eigenvalues λ=σ±iω\lambda = \sigma \pm i\omega where σ<0\sigma < 0 and ω>0\omega > 0. If the distance from any trajectory to the origin decreases by a factor of ee while the trajectory rotates through angle θ\theta, what is the relationship between σ\sigma, ω\omega, and θ\theta?
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