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" – 6y' + 25y = 0; y = e3x cos 4x When y = ex cos 4x, y' = y" = Thus, in terms of x, у" - бу" + 25у 3D + 25 e3x cos 4x

Calculus: Early Transcendentals
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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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Verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate interval I of definition for each solution.
у" - бу' + 25у %3D 0;
y = e3x cos 4x
When y = e3X cos 4x,
y'
=
y" =
Thus, in terms of x,
у" — бу' + 25у 3D
+ 25 e3x cos 4x
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. у" - бу' + 25у %3D 0; y = e3x cos 4x When y = e3X cos 4x, y' = y" = Thus, in terms of x, у" — бу' + 25у 3D + 25 e3x cos 4x
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