For what values of r does the function y= e^rx satisfy the differential equation 2y"+y'-y=0?

I am pretty sure that the soluton I share below is truly correct one : 

Then go to :
The next step you have to do is dividing all the items : 

Andddd here you are! that's the answer - r = -1, r = 1/2. Hope it's clear :) Regards.

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