show, by direct substitution, that the given functions y1(t) and y2(t) are solutions of the given differential equation. Then verify, again by direct substitution, that any linear combination Cy y1(t) + C2 y2(t) of the two given solutions is also a solution. y'' + 4y = 0, y1(t) = cos 2t, y2(t) = sin 2t

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 12CR
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show, by direct substitution, that the given
functions y1(t) and y2(t) are solutions of the given differential
equation. Then verify, again by direct substitution, that any linear combination Cy y1(t) + C2 y2(t) of the two given solutions is also a solution.

y'' + 4y = 0, y1(t) = cos 2t, y2(t) = sin 2t

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