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Economics Dynamics Problems 184

Economics Dynamics Problems 184 - 168 Economic Dynamics...

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168 Economic Dynamics Figure 4.16. Hence det( A λ I ) = λ 2 + 4 λ + 3 = ( λ + 3)( λ + 1) = 0, which leads to roots λ = r = − 3 and λ = s = − 1. Using these values for the eigenvalues, the eigen- vectors are v r = 1 1 and v s = 1 1 which gives the general solution x = c 1 e 3 t 1 1 + c 2 e t 1 1 or x ( t ) = c 1 e 3 t + c 2 e t y ( t ) = − c 1 e 3 t + c 2 e t The solution is illustrated in figure 4.17, 8 where the solution paths are revealed by the direction field, indicating quite clearly that the origin is a stable node.
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