438 Ordinary Differential Equationsdisplay the graph on t he rectangle R where 0 :::; x :::; 5 and 0 :::; y :::; 5. The
resulting phase-plane graph of y versus xis shown in Figure 10.11. The arrow
heads, point, and point coordinates which appear in this figure were added to
the output of SOLVESYS using illustrating software.
5
4
3 (2, 3)
y
2
1
0
(^0 1 2 3 4 5)
x
Figure 10. 11 Phase-Plane Plot of y versus x for System (8)We were able to produce the phase-plane portrait of y versus x shown
in Figure 10.12 by using our software PORTRAIT to solve the nine initial
value problems consisting of system (8) and the following set of nine initial
conditions on the interval [O, 2.5] and plotting the results on the same graph.
The initial conditions are
(i) x(O) = 0, y(O) = 2.5; (ii) x(O) = 0, y(O) = 3; (iii) x(O) = 0, y(O) = 5;
(iv) x(O) = 1.5, y(O) = O; (v) x(O) = 2, y(O) = O; (vi) x(O) = 5, y(O) = O;
(vii) x(O) = 5, y(O) = 3; (viii) x(O) = 1, y(O) = 5; and (ix) x(O) = 3, y(O) = 5.
The arrow heads, points, and points coordinates which appear in Figure 10.12
were added to the output of PORTRAIT using illustrating software.