I have a question in regard to the following;
considering the ODE
we can factor and find that the roots are $$r_1=r_2=i$$ and $$r_3=r_4=-i$$
So, I thought that a solution will be of the form $y(t)=c_1\cos(t)+c_2\sin(t)+c_3t\cos(-t)+c_4 t\sin (-t)$
but the answer given is the same except for it does not include the -t in the later two cos and sin.
I know that $cos(-t)=cos(t)$ but not for sin, so what is it I am doing wrong?