y''+16y=0

This is a DE that can be solved by Reduction of Order.  It is fairly straightforward, if not a bit tedious, mostly thanks to the trig derivatives and integrals.  I went about it the long way so as to help those struggling to understand and develop methodology for these sorts of ODE problems.

Of course, any questions or concerns (or typos or mistakes), feel free to write me and let me know!  Thanks and good luck!