Suppose that when a certain lake is stocked with fish, the birth and death rates B and 8 are both inversely proportional to √P. 1 (a) Show that P(t)=kt +. JP.) ² (b) If Po=121 and after 4 months there are 289 fish in the lake, how many will there be after 8 months? (a) Find the differential equation dP dt = P a b P √P dP dt where k is a constant. where ß= a √P and 8= b √P
Suppose that when a certain lake is stocked with fish, the birth and death rates B and 8 are both inversely proportional to √P. 1 (a) Show that P(t)=kt +. JP.) ² (b) If Po=121 and after 4 months there are 289 fish in the lake, how many will there be after 8 months? (a) Find the differential equation dP dt = P a b P √P dP dt where k is a constant. where ß= a √P and 8= b √P
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Suppose that when a certain lake is stocked with fish, the birth and death rates ß and 8 are both inversely
proportional to √P.
Ŝ
2
+ √PO) ².
(b) If P=121 and after 4 months there are 289 fish in the lake, how many will there be after 8 months?
(a) Show that P(t)=kt+√Po
(a) Find the differential equation
dP
dt
= P
P(t) =
sk my instructor
a
b
√P JP
F5 F6
h
Now solve the differential equation with the initial condition P(0) = Po and find P(t). Do not substitute in the numerical
value for Po-
#
8
-
F7
*
O
dP
dt
= +
F8
8
where k is a constant.
where B=
F9
11
B
a
√P
F10
+ 11
www
and 8 =
√i Vi
M
b
√P
F11
↓
F12
5.
Clear all
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PRTSC
INS
SCRLK
Mare
HOME
Check answer
PAUSE
8.3
PG UP
NUM
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