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let with suppose that dependent then there exist

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Unformatted text preview: m is equivalent to the equations Finally, upon setting , The corresponding eigenvector is Hence the general solution is x Invoking the initial conditions, It follows that , and . Hence the solution of the IVP is x 19. Set x . Substitution into the system of differential equations results in A which upon simplification yields is, A must satisfy A I 0 21. Setting x , 0 Hence the vector and constant results in the algebraic equations ________________________________________________________________________ page 373 —————————————————————————— CHAPTER 7. —— . For a nonzero solution, we must have A I the characteristic equation are and . With reduces to . The corresponding eigenvector is case , the system is equivalent to the equation It follows that x . The roots of , the system of equations For the . An eigenvector is and x The Wronskian of this solution set is xx . Thus the solutions are linearly independent for . Hence the general solution is x 22. As shown in Prob. , solution of the ODE requ...
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