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Growth
Authors: Bill Davis, Horacio Porta and Jerry Uhl
©19962007
Publisher: Math Everywhere, Inc.
Version 6.0
1.08 More Differential Equations
LITERACY
·
L.1)
Look at the differential equation
y
£
@
x
D
=
y
@
x
D I
2
+
Cos
@
x
D
2

y
@
x
DM
with y
@
0
D
=
1.
How do you know before you do any plotting that as x advances from 0, the plot of the
solution y
@
x
D
initially must go up?
·
L.2)
Look at the differential equation
y
£
@
x
D
=
y
@
x
D I
2
+
Sin
@
x
D
2

y
@
x
DM
with y
@
0
D
=
3.
How do you know before you do any plotting that as x advances from 0, the plot of the
solution y
@
x
D
initially must go down?
·
L.3)
Look at the differential equation
y
£
@
x
D
=
y
@
x
D I
2
+
Sin
@
x
D
2

y
@
x
DM
with y
@
0
D
=
1.
How do you know before you do any plotting that as x advances from 0, the plot of the
solution y
@
x
D
goes up near x's for which
2
+
Sin
@
x
D
2
>
y
@
x
D
and the plot of the solution y
@
x
D
goes down near x's for which
2
+
Sin
@
x
D
2
<
y
@
x
D
?
Why do you expect that the crests and dips of the plot of y
@
x
D
are located at places where
the y
@
x
D
plot crosses the plot of
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This note was uploaded on 10/11/2011 for the course MATH 241 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Kim
 Differential Equations, Equations

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