Math 2280 Exam 2
-
University of Utah
Spring 2013
Name:
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/+ionJ
This is a 50 minute exam. Please show all your work, as a worked
problem is required for full points, and partial credit may be rewarded for
some work in the right direction.
1
1. (25 points) Population Models
For the population model
=3P(5—P)
what are the equilibrium populations, and for each equilibrium poplu
ation determine if it is a stable or unstable. Draw the corresponding
phase diagram. Then, use separation of variables to solve the popu
lation model exactly with the initial population P(O) = 8.
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2. (20 points) Euler’s Method
Use Euler’s method with a step size h = 1 to calculate an approx
imate value for y(3), where y(x) is the solution to the initial value
problem
dy
d
—
=
y(O)
—3x y,
3.
3
3
/(-3
(oh)
x
-
4
/
More room for problem 2, if you need it.
5
3. (20 points) Higher Order Linear Homogeneous Differential Equations with
Constant Coefficients
Find the general solution to the differential equation:
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=
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