1550078481-Ordinary_Differential_Equations__Roberts_

Answers to S elect ed Exercises 563

9. d. 200 lbs. 100 lbs. They are equal.

11 (t) = (qi (t)) = 88 721 -. 0863104 t (-.921753)

. q ~w. e .~n~

+^420 ·^797 e -.00868956t (--.996690 .209652) + (200) 400

Limiting amounts: Tank A, 200 lbs.; Tank B, 400 lbs.

1 3. ( ( ) ( ) ( )

qA t) 0 0

q(t) = qB(t) = - 37333.35e-·^00025 t 0 -21000e-.ooo^5 t 1

qc(t) 1 - 2

• 
  
  
  
  4285. 71 e-.ooo7t ( -3I .5 ) + (4285 6000.00^71 )
        3.88889 12000.00
  
  
  
  

Limiting amounts:

Lake A , 4285.71 lbs.; Lake B, 6000 lbs.; Lake C, 12 , 000 lbs.

15. a. c' s r s Cs Rs C s

0 0 0 0

Vs Vs

c' m 0 rm 0 0 0 Cm Rm Cm

Vm Vm

c;,

r s rm rh

0 0

Rh Ch

vh Vii vh

Ch +

vh

0 0

rh re

0 R e Ce

c'

• e Ve Ve Ce Ve

0 0 0

re ro

R o Co

c' 0 Vo Va Co Vo

(^15) Cc(t). b. = kie-.251908t ( 0) ~ + k ( 0 ) ( 0 )
2 e-.732759t ~ + k 3 e-.08t ~
0 1 .898 045
1 -.449796 1.12987

• k 4 e-.0051724lt (.2J837) + kse-.0322034t (.93~336)
  .190011 .782666
  .166561 .770484