Show that the given function is a solution of the differential equation. y" + 25y = 0, y = cos(5x) + 5 sin(5x) Substituting y" and y into the original equation gives + 25(cos(5x) + 5 sin(5x)) = 0. The so
Show that the given function is a solution of the differential equation. y" + 25y = 0, y = cos(5x) + 5 sin(5x) Substituting y" and y into the original equation gives + 25(cos(5x) + 5 sin(5x)) = 0. The so
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F50b7307d-f147-4c39-812e-01e48cbfa721%2F36b3dc3d-fc1b-4969-afee-0198ba1d51fc%2F9fq1q2_processed.png&w=3840&q=75)
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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