1550078481-Ordinary_Differential_Equations__Roberts_

492 Ordinary Differential Equations

where the outflow rate from pond A to pond B is r 0 = 70 gal/hr. Thus, the

amount of salt in pond A satisfies

y~(t) = (.73)(100) - U'~

0

) (70) = 73 - .35y1.

A similar analysis shows that the amount of salt, Y2(t), in pond B satisfies

y;(t) = (;do) (70) - (;;

0

) (50) = .35y1 - .25y2

and the amount of salt, y 3 (t), in pond C satisfies

y~(t) = (;'~

0

) (50) - (;;

0

) (25) = .25y2 - .125y 3.

Initially, all three ponds contain no salt, so the initial conditions are Y1 (0) =

0 , Y2(0) = 0 , and y3(0) = 0. We used SOLVESYS to solve the system initial

value problem

y~ = Y1 (0) =^0

(1) Y2(0) = 0

on the interval [O, 20]. A graph showing the amount of salt in each pond on

the interval [O, 20] is shown in Figure 10.26.

400

300

200

100

5 10

t

15

Figure 10.26 Solution Graph for System (1)

20