Applications of Systems of Equations 4395 4 3 y 2 1 0
0 1 2 3 4 5
x
Figure 10.12 Phase-Plane Portrait for System (8)jcomments on Computer Software! For 1 :S i :S 10 , PORTRAIT will
attempt to solve numerically the i initial value problems consisting of the
autonomous, two component system initial value problem
dy1
dx = Ji (Y1, Y2)dy2
dx = f2(y1, Y2)and the initial conditions yl(ci) = d1i, y2(ci) = d2i on the interval [ai, bi]
where Ci E [ai, bi]. After the solut ion of an initial value problem has b een
calculated, you may elect for any initial value problem already solved (i) to
print the solution components on the monitor, (ii) to graph any subset
of the solution components in a rectangle R where ai ::; x ::; bi and
YMIN :S y :S YMAX where you select the values for YMIN and YMAX,
(iii) to produce a phase-plane portrait of any subset of IVPs already so lved
on any rectangle, (iv) to rerun the most recent initial value problem using a
different interval of integration or init ial conditions, or (v) input the initial
conditions for the next initial value problem to be solved. Complete instruc-
tions for using PORTRAIT appear in Appendix B.