7. The field mouse population in Example 1 satisfies the differential equation dy P dt 2 = - 450. a. Find the time at which the population becomes extinct if p(0) = 850. b. Find the time of extinction if p(0) = Po, where 0 < Po < 900. Nc. Find the initial population po if the population is to become extinct in 1 year.
7. The field mouse population in Example 1 satisfies the differential equation dy P dt 2 = - 450. a. Find the time at which the population becomes extinct if p(0) = 850. b. Find the time of extinction if p(0) = Po, where 0 < Po < 900. Nc. Find the initial population po if the population is to become extinct in 1 year.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
7 please
Transcribed Image Text:e
y
e
:)
2)
also differ only by a constant. Test this assumption by trying
to find a constant k such that y = y(t) + k is a solution of
equation (31).
c. Compare your solution from part b with the solution given in
the text in equation (17).
Note: This method can also be used in some cases in which the
constant b is replaced by a function g(t). It depends on whether you
can guess the general form that the solution is likely to take. This
method is described in detail in Section 3.5 in connection with second-
order equations.
20
sed
6. Use the method of Problem 5 to solve the equation
7. The field mouse
differential equation
dy
= -ay+b.
dt
population in Example 1 satisfies the
dy P
dt 2
-
450.
a. Find the time at which the population becomes extinct if
p(0) = 850.
b. Find the time of extinction if p(0) = Po, where 0 < Po <
900.
N c. Find the initial population po if the population is to
become extinct in 1 year.
8. The falling object in Example 2 satisfies the initial value
problem
dv
dt
a. Find the time that must elapse for the object to reach 98% of
its limiting velocity.
b. How far does the object fall in the time found in part a?
= 9.8 5' V(0) = 0.
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