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. (a) Write cos 3x + i sin 3x = e3ix = (cos x + i sin x)³ by Euler's formula, expand, and equate real and imag- inary parts to derive the identities cos x = } cos x + cos 3x, sin x = } sin x – sin 3.x. (b) Use the result of part (a) to find a general solution of y" + 4y = cos³ x.

. (a) Write cos 3x + i sin 3x = e3ix = (cos x + i sin x)³ by Euler's formula, expand, and equate real and imag- inary parts to derive the identities cos x = } cos x + cos 3x, sin x = } sin x – sin 3.x. (b) Use the result of part (a) to find a general solution of y" + 4y = cos³ x.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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. (a) Write cos 3x + i sin 3x = e3ix = (cos x + i sin x)³ by Euler's formula, expand, and equate real and imag- inary parts to derive the identities cos x = } cos x + cos 3x, sin x = } sin x – sin 3.x. (b) Use the result of part (a) to find a general solution of y" + 4y = cos³ x.
Transcribed Image Text:. (a) Write cos 3x + i sin 3x = e3ix = (cos x + i sin x)³ by Euler's formula, expand, and equate real and imag- inary parts to derive the identities cos x = } cos x + cos 3x, sin x = } sin x – sin 3.x. (b) Use the result of part (a) to find a general solution of y" + 4y = cos³ x.
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