Going over past exams (without solutions) I came across this question:
I work out using guess $y=\exp\lambda t$
By quadratic formula: $\lambda =-1 \pm2i$
$= \exp(t)\left( \exp(-1+2i) \right)$
But when I substitute the found $y$ into the original equation I don't identically get 0, and I'm not sure where I went wrong.
Thanks for your help.