Homework 4
Assignment Date:
Wednesday (02/23/2011)
Collection Date:
Wednesday (03/16/2011) (3/9/2011: Quiz1)
Grade:
Each problem is worth 10 points
Problem 4.1:
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
!
!
=
!
!
!
!
!
!
!
!
Problem 4.2:
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
!
!
+
!
cos
!
+
(
!
!
!
+
sin
!
)
!
!
=
0
Problem 4.3:
Consider a prolific animal whose birth and death rates,
!
and
!
,
are each
proportional to its population
with
!
>
!
and
!
!
=
!
!
=
0
.
(a) Compute the population as a
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