Exam 1, phase portraits, diff eq

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12 Terms

1
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both positive unique real eigenvalues
unstable nodal source
unstable nodal source
2
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both negative unique real eigenvalues
asymptotically stable nodal sink
asymptotically stable nodal sink
3
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opposite signs real eigenvalues
unstable saddle
unstable saddle
4
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1 eigenvalue\=0, 1 \> 0 both real
draw line of critical points, points going out
draw line of critical points, points going out
5
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1 eigenvalue\=0, 1 < 0 both real
draw line of critical points, going toward line
draw line of critical points, going toward line
6
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imaginary eigenvalues, constant < 0
asymptotically stable spiral sink (CCW)
asymptotically stable spiral sink (CCW)
7
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imaginary eigenvalues, constant \> 0
unstable spiral source (CW)
unstable spiral source (CW)
8
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imaginary eigenvalues, constant\=0
stable center (concentric circles)
stable center (concentric circles)
9
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repeated eigenvalues \> 0 DIAGONAL
unstable proper node
unstable proper node
10
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repeated eigenvalues < 0 DIAGONAL
asymptotically stable proper node
asymptotically stable proper node
11
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repeated eigenvalues \> 0, not diagonal
unstable improper node
unstable improper node
12
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repeated eigenvalues < 0, not diagonal
asymptotically stable improper node
asymptotically stable improper node