Studied by 13 people

5.0(1)

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Hint

1

stable improper node

2 distinct real roots,

λ1, λ2 < 0

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2

unstable improper node

2 distinct real roots,

λ1, λ2 > 0

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3

unstable saddle point

2 distinct real roots,

λ1 < 0 < λ2

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4

stable proper node

repeated roots with distinct eigenvectors

λ1 = λ2 < 0

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5

unstable proper node

repeated roots with distinct eigenvectors

λ1 = λ2 > 0

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6

stable improper node

repeated roots with only 1 eigenvector

λ1 = λ2 < 0

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7

unstable improper node

repeated roots with only 1 eigenvector

λ1 = λ2 > 0

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8

stable center point

pure imaginary complex conjugate roots

λ1 = λ2 = ± ai

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9

stable spiral point

pure imaginary complex conjugate roots

λ1 = λ2 = a ± bi

a < 0

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10

unstable spiral point

pure imaginary complex conjugate roots

λ1 = λ2 = a ± bi

a > 0

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11

stable improper node

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12

unstable improper node

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13

stable proper node

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14

unstable proper node

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15

stable center point

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16

unstable saddle point

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17

stable spiral point

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18

unstable spiral point

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