Finding k for y = cos(kt) to satisfy 4y'' = -25y

[afcwestwarrior]

Homework Statement

For what values of K does the function y=cos k t satisft the differential equation 4y"=-25y?



Do I have to find the derivative of y twice or what do i do

 

[rocomath]

... what does y'' mean?

 

[afcwestwarrior]

it means second order derivative I believe

 

[Tedjn]

Yes, find the second derivative and compare constants.

 

[afcwestwarrior]

ok so it would be y"=-k^2cos kt

 

[Tedjn]

Yes.

 

[afcwestwarrior]

then do i plug in values for it

 

[Gib Z]

You have 4y"=-25y. Substitute what you know to be y and y'', and equate coefficients as Tedjn said.