Please solve & show steps... for (a), please draw the graph.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Please solve & show steps... for (a), please draw the graph. 

Suppose that a certain population satisfies the initial value problem
dy
r(t)y – k, y(0) = Y0; where the growth rate r(t) is given by
dt
-
1+ sin t
r(t) =
and k represents the rate of predation.
3
1
a) Suppose that k =
Select the figure that represents y versus t
3
for yo = 0.5, 0.75, 1.
Choose one
b) Estimate the critical initial population y, below which the
population will become extinct.
NOTE: Round your answer to two decimal places.
Yc
Ye
10
c) Find a general relation between
k and the corresponding yc,
then plot ye versus k.
4
2
There is Choose onev
k
dependence of yYe on k.
Transcribed Image Text:Suppose that a certain population satisfies the initial value problem dy r(t)y – k, y(0) = Y0; where the growth rate r(t) is given by dt - 1+ sin t r(t) = and k represents the rate of predation. 3 1 a) Suppose that k = Select the figure that represents y versus t 3 for yo = 0.5, 0.75, 1. Choose one b) Estimate the critical initial population y, below which the population will become extinct. NOTE: Round your answer to two decimal places. Yc Ye 10 c) Find a general relation between k and the corresponding yc, then plot ye versus k. 4 2 There is Choose onev k dependence of yYe on k.
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