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# Recall that a second solution is obtained by

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Unformatted text preview: . The general solution is x ________________________________________________________________________ page 413 —————————————————————————— CHAPTER 7. —— All of the points on the line other points become unbounded. are equilibrium points. Solutions starting at all 3. Solution of the ODEs is based on the analysis of the algebraic equations . The characteristic equation is , the two equations reduce to One solution is x , with a single root . Setting . The corresponding eigenvector is . A second linearly independent solution is obtained by finding a generalized eigenvector. We therefore analyze the system . The equations reduce to the single equation , and a second linearly independent solution is Let . We obtain x Dropping the last term, the general solution is x ________________________________________________________________________ page 414 —————————————————————————— CHAPTER 7. —— 4. Solution of the ODE requires analysis of the algebraic equations...
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