Economics Dynamics Problems 76

Economics Dynamics Problems 76 - 60 Economic Dynamics...

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Unformatted text preview: 60 Economic Dynamics Figure 2.17. Or ay (t) + by (t) + cy(t) = 0 If we can find two linearly independent solutions9 y1 and y2 then the general solution is of the form y = c1 y1 + c2 y2 where c1 and c2 are arbitrary constants. Suppose y = e xt . Substituting we obtain ax2 e xt + bxe xt + ce xt = 0 e xt (ax 2 + bx + c) = 0 Hence, y = e xt is a solution if and only if ax2 + bx + c = 0 9 See exercises 9 and 10 for a discussion of linear dependence and independence. ...
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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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