Solve using De Moivre's Theorem to find the general solution.  y^(8) + 8y^(4) +16y=0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve using De Moivre's Theorem to find the general solution. 

y^(8) + 8y^(4) +16y=0 

 

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How did you get "pi / 4" when n is equal to eight? I have written the formula in red. 

r¹n [cos (0/n + 2πTK/n) +isin (0/n + 2TK/n)]
n= 8;r=4 ; 0= πT; K=
K=O
k=1
K=2
K=3
0,1,2,3,4,5,6,7
44 [cos (π/g + 0) + i sin ( T/8+0)]
Transcribed Image Text:r¹n [cos (0/n + 2πTK/n) +isin (0/n + 2TK/n)] n= 8;r=4 ; 0= πT; K= K=O k=1 K=2 K=3 0,1,2,3,4,5,6,7 44 [cos (π/g + 0) + i sin ( T/8+0)]
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