# Setting x results in the algebraic equations for a

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Unformatted text preview: distinct, the general solution is x The entire line along the eigendirection consists of equilibrium points. All other solutions diverge. The direction field changes across the line Eliminating the exponential terms in the solution, the trajectories are given by . 10. The characteristic equation is given by The equation has complex roots and solution vector must satisfy Substitution of A corresponding eigenvector is general solution is . For , the components of the . Thus the corresponding eigenvector is results in the single equation . Since the eigenvalues are distinct, the x 11. Setting x results in the algebraic equations ________________________________________________________________________ page 368 —————————————————————————— CHAPTER 7. —— . For a nonzero solution, we must have of the characteristic equation are have A , I and . Setting . The roots , we . This system is reduces to the equations A corresponding solution vector is given by the reduced system of equations is Setting , A corresponding solution vector is given by , the reduced system of equations is Finally, setting A corresponding solution vector is give...
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