This preview shows page 1. Sign up to view the full content.
Unformatted text preview: (a) x = c 1 e rt v 1 + c 2 e rt v 2 (b) x = c 1 e rt v + c 2 [ e rt t v + e rt v 2 ] Consider each case in turn. In example 4.9 we Found For two independent eigenvectors x ( t ) = c 1 e rt y ( t ) = c 2 e rt Hence, x / y = c 1 / c 2 is independent oF t and depends only on the components oF v r and v s and the arbitrary constants c 1 and c 2 . This is a general result and so all solutions lie on straight lines through the origin, as shown in fgure 4.21. In this case the origin is a proper node that is stable. Had the repeated root been positive, then we would have an unstable proper node. It is this situation we gave an example...
View
Full
Document
 Fall '11
 Dr.Gwartney
 Economics

Click to edit the document details