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Find all values of k for which the function y = sin(kt) satisfies the differential equation y" + 13y = 0. Separate your answers by commas.

Find all values of k for which the function y = sin(kt) satisfies the differential equation y" + 13y = 0. Separate your answers by commas.

Advanced Engineering Mathematics
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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Question
**Problem Statement** Find all values of \( k \) for which the function \( y = \sin(kt) \) satisfies the differential equation \( y'' + 13y = 0 \). Separate your answers by commas. **Explanation** In this problem, we are asked to determine specific values of the constant \( k \) such that the sinusoidal function \( y = \sin(kt) \) is a solution to the second-order linear homogeneous differential equation given by \( y'' + 13y = 0 \).
Transcribed Image Text:**Problem Statement** Find all values of \( k \) for which the function \( y = \sin(kt) \) satisfies the differential equation \( y'' + 13y = 0 \). Separate your answers by commas. **Explanation** In this problem, we are asked to determine specific values of the constant \( k \) such that the sinusoidal function \( y = \sin(kt) \) is a solution to the second-order linear homogeneous differential equation given by \( y'' + 13y = 0 \).
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