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Economics Dynamics Problems 205

# Economics Dynamics Problems 205 - Systems of rst-order...

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Systems of first-order differential equations 189 So long as solutions exist, then the packages will solve the system of equations. Thus, the system of three equations with initial values: x ( t ) = x ( t ) y ( t ) = x ( t ) + 3 y ( t ) z ( t ) z ( t ) = 2 y ( t ) + 3 x ( t ) x (0) = 1 , y (0) = 1 , z (0) = 2 (4.36) can be solved in a similar manner with no difficulty. In the case of nonlinear systems of differential equations, or where no explicit solution can be found, then it is possible to use the NDSolve command in Math- ematica and the dsolve(. . . , numeric) command in Maple to obtain numerical approximations to the solutions. These can then be plotted. But often more in- formation can be obtained from direction field diagrams and phase portraits. A direction field shows a series of small arrows that are tangent vectors to solutions
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