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AMS 361: Applied Calculus IV (DE & BVP)
Homework 4
Assignment Date:
Wednesday (02/25/2009)
Collection Date:
Wednesday (03/11/2009)
8:20AM
Grade:
Each problem is worth 10 points
Problem 4.1 (Prob 33, P. 76, 3E)
The following differential equation is of two different types
considered in Chapter 1separable, linear, homogenous, Bernoulli, exact, etc. Hence, derive
general solutions for the given equation in two different ways, and then reconcile your results
ௗ௬
ௗ௫
ൌെ
ଷ௫
మ
ାଶ௬
మ
ସ௫௬
.
Problem 4.2 (Prob 34, P. 76, 3E)
The following differential equation is of two different types
considered in Chapter 1separable, linear, homogenous, Bernoulli, exact, etc. Hence, derive
general solutions for the given equation in two different ways, and then reconcile your
results
ௗ௬
ௗ௫
ൌ
௫ାଷ௬
௬ିଷ௫
.
Problem 4.3
Consider a prolific breed of rabbits whose birth and death rates,
and
β
δ
, are each
proportional to the rabbit population
()
PP
t
=
with
>
and
ܲ
ൌܲሺݐൌ0ሻ.
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