- #1
Aerospace93
- 22
- 0
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...