if the condition in part is not satisfied that is

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Unformatted text preview: It follows that which is actually not dependent on the value of independent. Hence we must have a contradiction. 29 . Let 0 On the and 0 Based on the result of Part , , the vectors and are linearly , which leads to . It follows that and . In terms of the new variables, we obtain the system of two first order ODEs . The coefficient matrix is given by A Setting x results in the algebraic equations . For a nonzero solution, we must have A I . Multiplying both sides of the equation by , we obtain 30. Solution of the ODE requires analysis of the algebraic equations . For a nonzero solution, we must have A I . The characteristic equation is ________________________________________________________________________ page 378 —————————————————————————— CHAPTER 7. —— , with roots the system of equations reduces to Substitution of A corresponding eigenvector is general solution is and . With , . The corresponding eigenvector is results in the equation . Since the eigenvalues are distinct, the x Invoking the...
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