I am pretty sure that the soluton I share below is truly correct one :
[tex]y = e^(rx)
y' = re^(rx)
y'' = r^2e^(rx)[/tex]
Then go to :[tex]2y'' + y' - y = 0
2r^2 e^(rx) + r e^(rx) - e^(rx) =0[/tex]
The next step you have to do is dividing all the items :
[tex]2r^2 + r - 1 = 0[/tex]
Andddd here you are! that's the answer - r = -1, r = 1/2. Hope it's clear :) Regards.
