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(Reminder from Calculus) Here i is the imaginary unit. a) Use the Euler formula, e (cos(0) + i sin(0))" = cos(no) + i sin(no). b) Suppose y(t) = e-2teit solves y" + By' +C =0. What are B and C? cos(0) + i sin (0), to prove that for any n, we have

(Reminder from Calculus) Here i is the imaginary unit. a) Use the Euler formula, e (cos(0) + i sin(0))" = cos(no) + i sin(no). b) Suppose y(t) = e-2teit solves y" + By' +C =0. What are B and C? cos(0) + i sin (0), to prove that for any n, we have

Advanced Engineering Mathematics
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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**Reminder from Calculus:** Here \( i \) is the imaginary unit. a) Use the Euler formula, \( e^{i\theta} = \cos(\theta) + i\sin(\theta) \), to prove that for any \( n \), we have \( (\cos(\theta) + i\sin(\theta))^n = \cos(n\theta) + i\sin(n\theta) \). b) Suppose \( y(t) = e^{-2t}e^{it} \) solves \( y'' + By' + Cy = 0 \). What are B and C?
Transcribed Image Text:**Reminder from Calculus:** Here \( i \) is the imaginary unit. a) Use the Euler formula, \( e^{i\theta} = \cos(\theta) + i\sin(\theta) \), to prove that for any \( n \), we have \( (\cos(\theta) + i\sin(\theta))^n = \cos(n\theta) + i\sin(n\theta) \). b) Suppose \( y(t) = e^{-2t}e^{it} \) solves \( y'' + By' + Cy = 0 \). What are B and C?
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