This preview shows page 1. Sign up to view the full content.
Unformatted text preview: 44 Economic Dynamics We can summarise the method of isoclines as follows: (1) From the differential equation dy dx = ( x , y ) determine the family of isoclines ( x , y ) = m and construct several members of this family. (2) Consider a particular isocline ( x , y ) = m . All points ( x , y ) on this iso cline have the same slope m . Obtain the inclination = arctan m 180 Along the isocline ( x , y ) = m construct line elements with inclination . (This establishes part of the direction field.) (3) Repeat step 2 for each isocline. (4) Draw smooth curves to represent the approximate integral curves indi cated by the line elements of step 3. It is apparent that this is a very tedious procedure. Luckily, a number of mathe matical software packages now compute direction fields and can be used to con struct isoclines (see appendices 2.1 and 2.2). Example 2.12 dy dx = 2 x y In sections 2.11 and 2.12 we give the instructions on using software pack ages to solve this differential equation explicitly, and in appendices 2.1 andages to solve this differential equation explicitly, and in appendices 2....
View Full
Document
 Fall '11
 Dr.Gwartney
 Economics

Click to edit the document details