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

by Aerospace93
Tags: family, functions, number, solution, verify
 P: 22 1. The problem statement, all variables and given/known data (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. 3. 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...
HW Helper
P: 4,114
 Quote by Aerospace93 1. The problem statement, all variables and given/known data (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. 3. 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?
 P: 22 I believe you would if y''=-Ak2sinkt-Bk2coskt?
PF Patron