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

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
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 9E: Find the general solution for each differential equation. Verify that each solution satisfies the...
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Show that the given function is a solution of the differential equation:

y'' + 25y = 0,  y = cos(5x) + 5 sin(5x)

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Show that the given function is a solution of the differential equation.
y" + 25y = 0, y = cos(5x) + 5 sin(5x)
y" =
Substituting y" and y into the original equation gives
+ 25 (cos(5x) + 5 sin(5x)) = 0. The solution checks.
Transcribed Image Text:Show that the given function is a solution of the differential equation. y" + 25y = 0, y = cos(5x) + 5 sin(5x) y" = Substituting y" and y into the original equation gives + 25 (cos(5x) + 5 sin(5x)) = 0. The solution checks.
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