This preview shows page 1. Sign up to view the full content.
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. ...
View Full Document
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.
- Fall '11