y
xK3 K2 K1 0 1 2 3
K3
K2
K1
1
2
3
eCards:DifferentialEquations
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Differential Equations
Silvie Kuráňová
spring 2009
y
xK3 K2 K1 0 1 2 3
K3
K2
K1
1
2
3
y
xK3 K2 K1 0 1 2 3
K3
K2
K1
1
2
3
eCards:DifferentialEquations
AcroTEXeDucationBundle
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QUESTION
Sketch a direction field for the differential equation
y = x2
+ y2
− 1.
y
xK3 K2 K1 0 1 2 3
K3
K2
K1
1
2
3
eCards:DifferentialEquations
AcroTEXeDucationBundle
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Solution
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HELP
Question: Sketch a direction field for the differential equation
y = x2
+ y2
− 1.
Help: Start by computing the slope at several points. You can use
following table:
x -2 -1 0 1 2 0 1 2 0 1 2
y 0 0 0 0 0 1 1 1 2 2 2
slope
Now draw short line segments with these slopes at these points.
The more line segments you draw in a direction field, the clearer the
picture becomes.
y
xK3 K2 K1 0 1 2 3
K3
K2
K1
1
2
3
eCards:DifferentialEquations
AcroTEXeDucationBundle
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Other Question
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Solution
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SOLUTION
Question: Sketch a direction field for the differential equation
y = x2
+ y2
− 1.
Solution: After computing slopes at several points and drawing
short lines segments with these slopes at these points, we get graph
similar to Figure 1. More detailed direction field is shown in Figure 2.
y
xK2 K1 0 1 2
K2
K1
1
2
Figure 1
y
xK2 K1 0 1 2
K2
K1
1
2
Figure 2