(a) Write cos 3x C i sin 3x D e3ix D .cos x C i sin x/3 by
Chapter , Problem 43(choose chapter or problem)
(a) Write cos 3x C i sin 3x D e3ix D .cos x C i sin x/3 by Eulers formula, expand, and equate real and imaginary parts to derive the identities cos3 x D 3 4 cos x C 1 4 cos 3x; sin3 x D 3 4 sin x 1 4 sin 3x: (b) Use the result of part (a) to find a general solution of y00 C 4y D cos3 x:
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