So the problem is
y''+y=cosx y(0)=1 y(0)=-1
The roots are r^2=-1 (+i,-i)
so that would give a homogeneious equation of
but how do i figure out the other equation that i need? is it just as simple as y=Acosx?
if i go that route, then
plugging that into the original equation, i would get -Acosx+Acosx=cosx. cosx=0
that doesn't seem right at all. i'm confused on how to figure out how to pick the second equation.