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For the case the roots are both positive and the

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Unformatted text preview: nce one of the complex-valued solutions is given by ________________________________________________________________________ page 386 —————————————————————————— CHAPTER 7. —— x The other complex-valued solution is x . The general solution is x It is easy to see that all solutions converge to the equilibrium point 10. Solution of the system of ODEs requires that . The characteristic equation is , with roots . Substituting , the equations are equivalent to . The corresponding eigenvector is One of the complex-valued solutions is given by x Hence the general solution is x Invoking the initial conditions, we obtain the system of equations ________________________________________________________________________ page 387 —————————————————————————— CHAPTER 7. —— Solving for the coefficients, the solution of the initial value problem is x 11 . With x , the solution is x 11 . ________________________________________________________________________ pag...
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