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Math 293 Solutions to Problem Set 9.
§
1.3 #12
.
dy
dx
=
y
. The isoclines are obtained by setting
dy
dx
equal to a constant
c
, the slope of the slopeindicator
line segments all along the isocline. In the present case
the isoclines are the horizontal lines
y
=
c
, light red in the
ﬁgure (if you’re able to view the ﬁgure in color). Some
solutions are drawn in blue. The one passing through
(0
,

1) satisﬁes the initial condition
y
(0) =

1.
We can solve the equation
dy
dx
=
y
explicitly by separating
variables to get
y

1
dy
=
dx
. Integration then gives the
solutions
y
=
Ce
x
. The graphs of these functions are the
blue curves in the picture.
#13
.
dy
dx
=

x
y
. The isoclines are the curves

x
y
=
c
,or
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This homework help was uploaded on 01/21/2008 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, Differential Equations, Equations, Slope

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