# Verify every number of a family of functions is also a solution

## 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''=-k2coskt.
4(-k2coskt)=-25coskt; 4k2=25, so k=+/-5/2
(b) y= Asinkt+Bcoskt; y'= +/-Akcoskt+/-BKcoskt; y''= +-Ak2sinkt+/-bk2coskt
Im not sure how to verify this...

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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''=-k2coskt.
4(-k2coskt)=-25coskt; 4k2=25, so k=+/-5/2
(b) y= Asinkt+Bcoskt; y'= +/-Akcoskt+/-BKcoskt; y''= +-Ak2sinkt+/-bk2coskt
Im not sure how to verify this...
Well, do you have 4y'' = -25y or not?

I believe you would if y''=-Ak2sinkt-Bk2coskt?

HallsofIvy