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Economics Dynamics Problems 148

# Economics Dynamics Problems 148 - {x[t>a t C[1 which is...

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132 Economic Dynamics Figure 3.21. solvers. One difference is shown immediately by attempting to solve the recursive equation x t = ax t 1 . The input and output from each programme is as follows. Mathematica RSolve[x[t]==ax[t-1],x[t],t] {{x[t]->a 1+t C[1] Maple rsolve(x(t)=a*x(t-1),x(t)); x(0)a t While Maple ’s output looks quite familiar, Mathematica ’s looks decidedly odd. The reason for this is that Mathematica is solving for a ‘future’ variable. If the input had been RSolve[x[t+1]== ax[t],x[t],t] Then the solution would be
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Unformatted text preview: {{x[t]->a t C[1]}} which is what we would expect. Note also that while Mathematica leaves unsolved the unknown constant, which it labels C[1], Maple assumes the initial condition is x (0) for t = 0. If attempting to solve y t = ay t − 1 + by y − 2 for example, then when using Mathematica , this should be thought of as y t + 2 = ay t + 1 + by t when solving for y t . With this caveat in mind, we can explore the RSolve and rsolve commands in more detail....
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