I am trying to find what values of r in $y = e^{rx}$ satsify $2y'' + y' - y = 0$
I thought I was being clever and knew how to do this so this is how I proceeded.
$y' = re^{rx}$ $y'' = r^2 e^{rx}$
$2(r^2 e^{rx}) +re^{rx} -e^{rx} = 0 $
I am not sure how to proceed from here, the biggest thing I am confused on is that I am working with a variable x, with no input conditions at all, and a variable r (the constant) so how do I do this?