based on part the equations reduce to the single

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Unformatted text preview: olution may be written as x 7. Solution of the ODE requires analysis of the algebraic equations . For a nonzero solution, we must have A I . The only root is , which is an eigenvalue of multiplicity two. Substituting into the coefficient matrix, the system reduces to the single equation . Hence the corresponding eigenvector is One solution is x . For a second linearly independent solution, we search for a generalized eigenvector. Its components satisfy ________________________________________________________________________ page 416 ————————————————————————— CHAPTER 7. —— , that is, . Let , some arbitrary constant. Then It follows that a second solution is given by x Dropping the last term, the general solution is x Imposing the initial conditions, we require that , which results in and Therefore the solution of the IVP is x ________________________________________________________________________ page 417 —————————————————————————— CHAPTER 7. —...
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