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# All other solutions diverge the direction field

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Unformatted text preview: nt on x x . It follows that , for . ________________________________________________________________________ page 365 —————————————————————————— CHAPTER 7. —— Section 7.5 2. Setting x , and substituting into the ODE, we obtain the algebraic equations . For a nonzero solution, we must have A I . The roots of the characteristic equation are and . For , the two equations reduce to . The corresponding eigenvector is Substitution of results in the single equation . A corresponding eigenvector is Since the eigenvalues are distinct, the general solution is x 3. Setting x results in the algebraic equations . For a nonzero solution, we must have A I . The roots of the characteristic equation are and . For , the system of equations reduces to . The corresponding eigenvector is Substitution of results in the single equation . A corresponding eigenvector is Since the eigenvalues are distinct, the general solution is x ________________________________________________________________________ page 366 —————————————...
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