1. Nov 18, 2009

### dwilmer

In Boyce and Diprima textbook it says that:

mu'' + ku = 0 .

Then it says the general solution of this is:

u = Acos (w^2)t + B sin (w^2)t , where w^2 = k/m

It provides no explanation how it arrives at this. Where does the cos and sin come from?????

PS: it is supposed to be the greek letter w, whatever that is called and it also has a sub-0 on it, but i didnt include it because it looks confusing without the right fonts.

2. Nov 18, 2009

### tiny-tim

Welcome to PF!

Hi dwilmer! Welcome to PF!

(have a little omega: ω and try using the X2 tag just above the Reply box )
Because [cos(ωt)]'' is obviously -ω2cos(ωt), and [sin(ωt)]'' is obviously -ω2sin(ωt)

3. Nov 18, 2009