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Economics Dynamics Problems 200

# Economics Dynamics Problems 200 - Example 4.18 Consider...

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184 Economic Dynamics Figure 4.32. The procedure generalises quite readily to systems of equations. Let dx dt = f ( x , y ) dy dt = g ( x , y ) (4.32) denote a system of autonomous differential equations and let the initial value of the system be x ( t 0 ) = x 0 and y ( t 0 ) = y 0 . Then x 1 = x 0 + f ( x 0 , y 0 ) ± t y 1 = y 0 + g ( x 0 , y 0 ) ± t (4.33) which can be repeated for further (approximate) values on the solution curve. For an autonomous system in which y = φ ( x ), then such a procedure allows us to plot the trajectory in the phase plane.
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Unformatted text preview: Example 4.18 Consider example 4.6 given by the differential equations: dx dt = f ( x , y ) = − 2 x − y + 9 dy dt = g ( x , y ) = − y + x + 3 with x ( t ) = 2 and y ( t ) = 2. Given these values, and letting ± t = . 01, then f ( x , y ) = − 2(2) − 2 + 9 = 3 g ( x , y ) = − 2 + 2 + 3 = 3...
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