Economics Dynamics Problems 180

Economics Dynamics Problems 180 - 164 Economic Dynamics...

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164 Economic Dynamics Substituting all these results into the differential equation system we have e 2 t (2 t + 2 v 1 + 1) = e 2 t ( t + v 1 ) e 2 t ( t + v 2 ) e 2 t ( 2 t + 2 v 2 1) = e 2 t ( t + v 1 ) + 3 e 2 t ( t + v 2 ) Eliminating e 2 t and simplifying, we obtain v 1 + v 2 =− 1 v 1 + v 2 1 which is a dependent system. Since we require only one solution, set v 2 = 0, giving v 1 1. This means solution x 2 is x 2 = e 2 t t ± 1 1 ² + e 2 t ± 1 0 ² Hence, the general solution is x = c 1 e 2 t ± 1 1 ² + c 2 ³ e 2 t t ± 1 1 ² + e 2 t ± 1 0 ²´ or x = c 1 e 2 t + c 2 ( t 1) e 2 t y c 1 e 2 t c 2 te 2 t 4.7 Solutions with complex roots For the system ˙x = Ax with characteristic equation det( A λ I ) = 0 , if tr( A ) 2 < 4det( A ), then we have complex conjugate roots. Return to our situation of just two roots,
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This note was uploaded on 12/14/2011 for the course ECO 3023 taught by Professor Dr.gwartney during the Fall '11 term at FSU.

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