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Unformatted text preview: To verify this, deFne the following transformation: v = k 1 . . . dv dt = (1 ) k dk dt or k = k (1 ) dv dt Using these results we can derive the following k k + ( n + ) kk = sa k k + ( n + ) k 1 = sa k k 1 dv dt + ( n + ) v = sa i.e. dv dt + (1 )( n + ) v = (1 ) sa which is a linear differential equation in v with solution v ( t ) = as n + + v as n + e (1 )( n + ) t 2 A Bernoulli equation takes the general form dy dt + f ( t ) x = h ( t ) x See Giordano and Weir (1991, pp. 956)....
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- Fall '11