I just arrived to an extremely weird ODE and I was wondering how could I solve it: $$ y'(x)+2y(x)+3y(-x)=0. $$ Actually, I am not even sure if it is possible to prove that it has a unique solution (provided an initial condition). I tried to put it on wolfram alpha but I didn't get anything. My first thought was to use "separation of variables" method but I don't think that it will help because of the term $y(-x)$. Actually I am completely clueless.
Edit: I am actually wondering if this ODE has non-symmetric solutions, that is, neither odd nor even solutions.