(b) Plot of Numerical Solution Curve and Direction Field

The data points can be used to create an approximate phase portrait as follows:

> ptsXY := [ seq( [ pt[2], pt[3] ], pt=ptsE ) ]:

> XYplot := plot( ptsXY, color = GREEN, thickness = 2 ):

>

The direction field is produced in the usual way:

> DOMAIN := t = 0 .. 1.75 ; # specify reasonable interval for indep vars

> WINDOW := x = -3 .. 2,

> y = -2 .. 1 ; # specify reasonable intervals for all dependent vars

>

> DIRplot := DEplot( MODEL, VAR, DOMAIN, WINDOW, arrows = MEDIUM ):

>

> display( [ DIRplot, XYplot ],

> title = `Direction Field and Euler Solution for #6` );

>