edit: you aren't proving it's LTI, you proving it COULD be lti 1. The problem statement, all variables and given/known data the question: could the following system be LTI? x(t)=-5cos(2t) --> y(t)=exp(-2tj) 2. Relevant equations the chapter is about eigenfunctions of LTI systems, wich are of the form exp(st). 3. The attempt at a solution So my guess for what i had to do, was find a transfer function H(s), so that H(s)*x(s)=y(s). so i wrote x(t) as follows: x(t)=-5/2(exp(2*t*j)+exp(-2*t*j) so x(2)=-5/2(exp(st)+exp(-st)) with s=2j. so than i thought, H(s)=y(s)/x(s), but y and x are still functions of t, so i don't know what to do now... and btw laplace isn't explained untill the next chapter so i'm not supposed to use that. the given answer is 'yes (H(s=2j)=0)'. so i think i do indeed need to do something with the transfer function.