Constant Coefficient and Equidimensional Special Cases

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10 Terms

1
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undamped oscillator (standard case)

a0 = 0, b0 > 0; imaginary roots

2
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undamped

 a0 = 0, b0 < 0

3
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overdamped

a02 > 4b0

4
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underdamped

a02 < 4b0

5
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critically damped

a02 = 4b0

6
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(a0 − 1)2 > 4b0

real and unequal roots; standard solution

7
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(a0 − 1)2 = 4b0

repeated root; second term has xlnx

8
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a0 = 1; s1,2 = = ±i √b0

cosines and sines

9
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(a0 − 1)2 < 4b0

complex roots, x^s times cosines and sines

10
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β

½ [4b0 − (a0 − 1)2 ]1/2 .