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# X therefore the general solution is x the solution

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Unformatted text preview: initial conditions, we obtain the system of equations Hence and , and the solution of the IVP is x . . Both functions are monotone increasing. It is easy to show that and provided that 31 . For , solution of the ODE requires that . The characteristic equation is . With , with roots and , the system of equations reduces to . The corresponding eigenvector is Substitution ________________________________________________________________________ page 379 —————————————————————————— CHAPTER 7. —— of results in the equation . An eigenvector is The general solution is x The eigenvalues are distinct and both . For The equilibrium point is a stable node. , the characteristic equation is given by and . With reduces to , with roots , the system of equations . The corresponding eigenvector is Substitution of results in the equation is . An eigenvector The general solution is x The eigenvalues are of opposite sign, hence the equilibrium point is a saddle...
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