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a) Use the Euler formula, e¹⁰ (cos(0) + i sin(0))" = cos(n) + i sin(n). b) Suppose y(t) = e-2t eit solves y" + By' + C = 0. What are B and C? = cos(0) + i sin(0), to prove that for any n, we have

a) Use the Euler formula, e¹⁰ (cos(0) + i sin(0))" = cos(n) + i sin(n). b) Suppose y(t) = e-2t eit 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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Here i is the imaginary unit.
a) Use the Euler formula, e^(iθ) = cos(θ) + i sin(θ), to prove that for any n, we have
(cos(θ) + i sin(θ))^n = cos(nθ) + i sin(nθ).
b) Suppose y(t) = e^(−2t)e^(it) solves y′′ + By′ + C = 0. What are B and C?

a) Use the Euler formula, ei = (cos(0) + i sin(0))" = cos(nº) + i sin(nº). b) Suppose y(t) = e-2t eit solves y" + By' + C = 0. What are B and C? cos(0) + i sin(0), to prove that for any n, we have
Transcribed Image Text:a) Use the Euler formula, ei = (cos(0) + i sin(0))" = cos(nº) + i sin(nº). b) Suppose y(t) = e-2t eit solves y" + By' + C = 0. What are B and C? cos(0) + i sin(0), to prove that for any n, we have
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