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Prelim 1
Math 2930
Spring 2009
show work, 6 problems, no calculators
1a)
(4 points)
Write your name and section number at the top of this page.
1b)
(10 points)
Solve the diﬀerential equation
y
±
+
1
5
y
=
e

t
for
y
(
t
) having
initial value
y
(0) = 5.
1c)
(6 points) (1c is not related to 1b)
Find a function
f
(
x, y
) so that the
exact equation
2
x
2
ydx
+
2
3
x
3
dy
= 0
says
df
= 0.
1
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(16 points)
A virus infects a population of 10000 individuals as follows. Let
x
(
t
) be the number of infected, which we model as a diﬀerentiable function.
The rate at which
x
is increasing is proportional to the product of the number
of infected and the number of uninfected. Initially 50 are infected and the
rate when
x
= 250 is 25 per month.
Write the diﬀerential equation for
x
(
t
). Find the equilibrium solutions and
determine their stability.
You are not asked to solve the equation.
2
3)
(16 points)
Consider the second order diﬀerential equation
y
±±
=

y
3
with
initial conditions
y
(0) = 0, and
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This note was uploaded on 01/21/2011 for the course MATH 2930 taught by Professor Terrell,r during the Spring '07 term at Cornell University (Engineering School).
 Spring '07
 TERRELL,R
 Math

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