Unformatted text preview: To verify this, deFne the following transformation: v = k 1 − α . . . dv dt = (1 − α ) k − α dk dt or ˙ k = k α (1 − α ) dv dt Using these results we can derive the following k − α ˙ k + ( n + δ ) kk − α = sa k − α ˙ k + ( n + δ ) k 1 − α = sa ± k − α k α 1 − α ² dv dt + ( n + δ ) v = sa i.e. dv dt + (1 − α )( n + δ ) v = (1 − α ) sa which is a linear differential equation in v with solution v ( t ) = as n + δ + ± v − as n + δ ² e − (1 − α )( n + δ ) t 2 A Bernoulli equation takes the general form dy dt + f ( t ) x = h ( t ) x α See Giordano and Weir (1991, pp. 95–6)....
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 Fall '11
 Dr.Gwartney
 Economics, Derivative, Economic Dynamics, Bernoulli equation,2

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