EC 473 1 7 7

c - a a - cp,-=-.b - d d - b

uilz

EC473 179

Qd = a+bP (1)

Qs = c+dt’ (2)

b d

d&ad = be’-bc+bdt

ad-bc+bdt = bc-ad-bdtP= db b - d

F = bc-ab-bdt = c-a-dtb(b-d) b-d I

180 EC 473

hl c - a - d t c - a -dt dtp-p,---=-=-

LItl~pq=bc-ad%& bc&d4&-%dtd-b- =- =-

b-a’ b - d b - d dd

11.2.3 tl5d Dynamic

dU fd~6~WhtW~~%U~~~~$J (Cobweb model)

Ql= a+b‘P,

Q:= c+@-,

Q:'=Q:~lt5ldlKh.lfll5 Solve nlFillnihtl5tii Static15lIl~lk;a'l

a+bP, = e+dP,,

bP;dP,, = c - a

c - a

b

Q,d = Q,!, = = e = = Q;m, = Q;

a - c c - ap=-=--d - b b - d

a d - b c&--d - b

EC 473 181

e: =a+bc

Q:= c + et-2

Q”=Q:

a - c c - aji=-=--

d - b b - d

182 EC 473

Q: = c+dp,-,QUHI time path lNlu5lpll rmi Jkttwhu3i iterative method

%I

oifmfm~ (1) hpanino=W

s =a+bF

tTUn1r~ (l)-(3) o&M

(2)

(3)

(I;“-e=b(+F) (4)

‘b(pt - p) = d(P,-, - F)

EC 473 1 8 3

1Xil

0

1

2

3

*

Slfll ¶J3WfU

e-3; a-i?

1 8 4 Ek ‘473

do General Solution = Complemehary Fupction + Particular Intigral

Y, = Y6tYP

Y = A(-a)t + c l&J a#-1-l+a

uns Y = A(-a)+ct = A+ct dFl a=-1

EC 473 1 8 5

6lfE Y,

0) = (2)

uie

Auu8b a

H%m.ldl

odl

= (Yo -2 )(-a)‘+ c &f-l

1+a l+a

= no - c)+ct \ Ids a = -1

l+a

= yo+ct

Q: = a+bP, (1)

Qt = *t-l (2)

a+bp, = c+dp,l

bPt+dPe, = c-a

P. t+l -dp = c-a- -.b b

Yl+aYwI : = C

= - d m c = c - a

-T b

c-a 6au P

IdU time path 3WilhfdhilUXUWlJ Iterative

186 EC 473

rm3mii Y,,-Y, = 2

EC 473 1 8 7

11.4 flldtY9lfU~ First Order Differential Equation

fI1dtlUf11~ First Order Differential Equation Il%fll5tllfllti??l (time Path) fBS$

~~‘?a~~~l~~~~ll~~l~U~~i?a~S6~~~dQ~~Q~(Con~uo~ variable) hkh~1~~=tW~l5&if

$El du-g+aY=b (1) hcf a,b duha~ff

general solution = particular integral + complimentary function

ThAlfNl Partieular iatcgral = YP

%RtJ$n’ Y, = K huff K 6dUfilA~~

h-su”U dy .d.K-=-= o

dt dt

IIWUPII Y = K Ml: dY/dt = 0 ~(1) .oz?#

0 + aK = b

+?Fl K = b/a

lh%O~%# particular integral = ‘Y, = K = b/a (a f 0)

~01dThll¶Hl Complementary fkction (Y,)

hl &IWl¶JfIlS~(l) %hJ$UJ~us differential equation

wviz+q=o

uie$dY = -adt

188

de C=dltw~

EC 473

L 1uunQ e-&

ilu deftite sohtion &l dll time path lJ89 Y

v&l &=-aY+b

81 a > 06ln~~ilnla~Ue~YnjaY, WiTNJldl~ (converge2ux) QNJnlWM

EC 473 189

14; time path iitl r,=( I

u, -p+Ea

dUllllUfil a = 2lklZ b - 6 hU Y,,=O

odbi

Y,=7e-‘+3 l9U time path

-..----..-.--..-..----..-..-..--.-..-..-

190 EC 473

n) Y,, = Y, + 1 cr,=lO>

U) Y,, = aY, V,,=W

n) Y,, + 3Y, = 4 0+4

4 y,, = 0.2Y, + 4 cro=4>

Q) 2y*, - Y, = 6 01,=7)

1. nIn%hfI?thIfl~8 18J~0i5flliiinElarmnJu~qnanirro=lilurriuh

2. WHI general solution lln~dehitesohhon QInPfun~s di@erential dbhd

n) dYidi + 4Y = 12 (Y,=a

U) dYldt + 1OY = 15 cr,=o)

f0 dYldt - 2Y = 0 cr,-9>

J) 2dYldt + 4Y = 6 cr,-0

3. o&mfuIiI time path ldu 3 iin’nuturnI~i~udqnanIneliI~‘lr

4 . oiniiuudine~icr~rr~rnnm~u~ni~

Y, = c, + I,

c, =- 150 + 0.7Y+, ’

fhfw11X y. = i 200 iin:: I, = 100

wii time path w14 Yt iin: 12, rin:n’cireriAiuiii9uqnanm~iil~~iirrrn~rmiol~6. oiniiYubine~iffru~ffinPl~unni~

Y, = c, + 4 + ct

c, = 150 +0.7(dY/dt)

4 I 50

G, = 80

----..-..-..--.- ..-. --..-..- __-..-..-.

E C 4 7 3 191