You are beginning to draw a phase portrait for a system of two equations. You know th x(0) = 1 and that y(0) = 1. You also know that x' = 0.5 and that y' = -1 at that point. Which of the following graphs correctly depicts the start of this phase portrait? 2.0 1.5

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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You are beginning to draw a phase portrait for a system of two equations. You know that
x(0) = 1 and that y(0) = 1. You also know that x' = 0.5 and that y' = −1 at that
point. Which of the following graphs correctly depicts the start of this phase portrait?
2.0
1.5
a) 1.0
0.5
0.0
2.0
y
1.5
○ b) 1.0
О
0.5
x
0.5
1.0
1.5
2.0
x
0.0
0.5
1.0
1.5
2.0
2.0
1.5
y
C) 1.0
0.5
x
0.0
0.5
1.0
1.5
2.0
2.0
1.5
○ d) 1.0
0.5
x
0.0
0.5
1.0
1.5
2.0
Transcribed Image Text:You are beginning to draw a phase portrait for a system of two equations. You know that x(0) = 1 and that y(0) = 1. You also know that x' = 0.5 and that y' = −1 at that point. Which of the following graphs correctly depicts the start of this phase portrait? 2.0 1.5 a) 1.0 0.5 0.0 2.0 y 1.5 ○ b) 1.0 О 0.5 x 0.5 1.0 1.5 2.0 x 0.0 0.5 1.0 1.5 2.0 2.0 1.5 y C) 1.0 0.5 x 0.0 0.5 1.0 1.5 2.0 2.0 1.5 ○ d) 1.0 0.5 x 0.0 0.5 1.0 1.5 2.0
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