Hello everyone! (Merry Christmas and happy holidays)

I got to solve

-y'' + y = 0

I'm so lost.

I tried cos(x) and sin(x)

then i tried y = sin(-x) => y' = -cos(-x) => y'' = -sin(-x)

=> $\displaystyle -y'' + y = -(-sin(-x))+ sin(-x) = sin(-x)+sin(-x) = -2 sin(x) \not= 0$

The solution is not that obvious, I guess.

Does anyone knows the solution?

Kind regards,

Rapha