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Math 3301
Homework Set 2
10 Points
For problems 1 & 2 find the solution to the given IVP and determine the interval of validity for the
solution.
Any approximate answers must be to at least the 4
th
decimal place and you may need
computational aids in finding some of the intervals of validity.
Separable Differential Equations
1.
( )
25
01
83
x
yy
y
−
′ =
=
+
2.
( )
3
08
78
y
xx
′
=
=
+
3.
Solve the following differential equation and determine the minimum value(s) of the solution.
Any
approximate answers must be to at least the 4
th
decimal place.
You may assume that
0
y
>
.
( )
( )
2
1
03
x
y yx x
y
−
′
=
−=
e
For problems 4 & 5 you MUST set up and solve the appropriate IVP(s) in order to receive any credit for
the problem.
Any decimals must be to at least the 4
th
decimal place.
Modeling, Part I
4.
A 1000 gallon tank contains 800 gallons of water with 45 ounces of dye dissolved in it.
Water with a
dye concentration of
( )
100
10 2
t
ct
−
=
−
e
ounces/gal is flowing into the tank at a rate of
6 gallons/min
and a well mixed solution flows out at a rate of 6 gallons/min.
If left to forever, what would be the
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This note was uploaded on 03/13/2009 for the course MATH 2171 taught by Professor Deng during the Spring '08 term at UNC Charlotte.
 Spring '08
 Deng
 Differential Equations, Equations

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