Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Show that the given function is a solution of the
y'' + 25y = 0, y = cos(5x) + 5 sin(5x)
**Please see attachment
![Show that the given function is a solution of the differential equation.
\[ y'' + 25y = 0, \quad y = \cos(5x) + 5 \sin(5x) \]
\[ y'' = \boxed{} \]
Substituting \( y'' \) and \( y \) into the original equation gives
\[ \boxed{} + 25(\cos(5x) + 5 \sin(5x)) = 0. \] The solution checks.](https://content.bartleby.com/qna-images/question/50b7307d-f147-4c39-812e-01e48cbfa721/36b3dc3d-fc1b-4969-afee-0198ba1d51fc/9fq1q2_processed.png)
Transcribed Image Text:Show that the given function is a solution of the differential equation.
\[ y'' + 25y = 0, \quad y = \cos(5x) + 5 \sin(5x) \]
\[ y'' = \boxed{} \]
Substituting \( y'' \) and \( y \) into the original equation gives
\[ \boxed{} + 25(\cos(5x) + 5 \sin(5x)) = 0. \] The solution checks.
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