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3.1 Theory of linear equations 3.3 Homogeneous linear equations with constant coefficients 3.4 Undetermined coefficients
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① )daff ,÷
=
Put -
P
,
P > o
P
a) increasing pop
Os Lil
b) P
decreasing
s it
pop
c) PCO ) -
3 PC 61 ) = ?
I
dp =
-8 at
P ( Il -
P) 1100 P =
" 't
cel"
(I ) 'd "
+
at it
(2/25)
61,4
P ( 61 ) 11
zg
= .
e
( Int pl In Ill pl ) =
2- t + C 1425761
3g
- -
, + e.
275
In IPI -
In 111 - P I =
2- t t C P 161 ) =
10.7816
25
t.iq/=zettc
"
h
=
e(21254 -1C
25¥
Ce
1¥
=
( " 5) t (2125)t
P =
lice -
pce
(425 ) t
25) t
P ( I t Ce ) =
, ice
(21255L
P =
(2/25) -L
I + Ce
3 = 11C
-
I + C
3 -13C =
11C
C = 3
-
8
, ② initial 400 fish PCO) =
400
Max 3000 fish K =
3000
doubled first PCI ) = 800
in
year
⑨
( _P
)
KP
adit
= l -
PH ) = 3000
Kt
3000 I -16.5 e-
Pl ' ) 800
|p
=
"t
soo = 3000
- K
I -16.5 e
- K
30001N
I -16.5 e =
I IP 30001
IP -
In -
=
Kt -1C 800
K
(pf↳ )
-
In =
Kt t C e = 0.423076923
⑨ K =
0.86
=P = Cekt
P -
3000 ② Pct ) =
1500
I = P -
3000 1500 =
3000
-08Gt
Cekt 1+6 .se
Kt
)
0.8Gt
(
-
Ce
-
3000 =p i t I -16.5 e = 2
-
O 8£
Plt ) 3000
-
= 6.5 e =
I
- Kt
I t Ce
-
0.8Gt
e =
1-
Plo ) = 400 6.5
400 = 3000 -
0.861 = -
1.8718
I + C
t = 2.1765
400 -1400C =
3000
C =
6.5
PH ) = 3000
Kt
I -16.5 e-
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