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Economics Dynamics Problems 129

Economics Dynamics Problems 129 - Discrete dynamic systems...

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Discrete dynamic systems 113 Hence c 3 = y 0 c 4 = y 1 r c 3 = y 1 ry 0 r Therefore, the general solution satisfying the two initial conditions, is y n = y 0 r n + y 1 ry 0 r nr n Example 3.11 (equal real roots) Let y n + 2 = 4 y n + 1 4 y n This has the characteristic equation x 2 4 x + 4 = ( x 2) 2 = 0 Hence, r = 2. y n = c 3 (2) n + c 4 n (2) n Suppose y 0 = 6 and y 1 = 4, then c 3 = y 0 = 6 c 4 = y 1 ry 0 r = 4 (2)(6) 2 = − 4 Hence, the particular solution is y n = 6(2) n 4 n (2) n which tends to minus infinity as
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