Economics Dynamics Problems 55

# Economics Dynamics Problems 55 - Continuous dynamic systems...

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Continuous dynamic systems 39 Furthermore, if we have the initial condition that y (0) = y 0 , then we can solve for c y 0 =− a b + c c = y 0 + a b Hence, we have the solution to the initial value problem of y ( t ) a b + ± y 0 + a b ² e bt Example 2.11 Suppose we have the initial value problem dy dt = 2 y + 4 ty (0) = 1 Applying the four-step procedure we have Step 1 2 y = 4 t Step 2 µ ( t ) = e ³ 2 = e 2 t Step 3 e 2 t y = ´ 4 te 2 t + c Step 4 e 2 t y 2 te 2 t e 2 t + c Or y 2 t 1 + ce 2 t Since y (0) = 1, then 1 1 + c c = 2 Hence, y ( t ) 2 t 1 + 2 e 2 t 2.3 Compound interest If an amount A is compounded annually at a market interest rate of
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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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