Verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate interval I of definition for each solution. y" - 4y + 13y = 0; y = e²x cos 3x When y = e2x cos 3x, y' = y" = Thus, in terms of x, y" - 4y' + 13y = + 13e²x cos 3x

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate interval I of definition for each solution.
y" - 4y' + 13y = 0; y = e2x cos 3x
When y = e2x cos 3x,
y' =
=
y":
Thus, in terms of x,
y" - 4y' + 13y =
11
+ 13e²x cos 3x
Transcribed Image Text:Verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate interval I of definition for each solution. y" - 4y' + 13y = 0; y = e2x cos 3x When y = e2x cos 3x, y' = = y": Thus, in terms of x, y" - 4y' + 13y = 11 + 13e²x cos 3x
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