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## Homework Statement

(a)For what values of k does the function y=coskt satisfy the differential equation 4y''=-25y?

(b) For those values of k, verify that every number of the family of functions y=Asinkt+Bcoskt is also a solution.

## The Attempt at a Solution

(a) y=coskt, y'=-ksinkt, y''=-k

^{2}coskt.

4(-k

^{2}coskt)=-25coskt; 4k

^{2}=25, so k=+/-5/2

(b) y= Asinkt+Bcoskt; y'= +/-Akcoskt+/-BKcoskt; y''= +-Ak

^{2}sinkt+/-bk

^{2}coskt

Im not sure how to verify this...