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.

In all honesty, there really is no “work” per say to show. mainly it’s just using the process of elimination. the question is asking which domain(s) would be the most appropriate for the function c(n). n is the number of observed vehicles so right away, 1, 2, and 3 can be eliminated.why? 1, 2 start in the negatives and therefore it is impossible to observe negative cars. so, #4 would be the best answer to the given problem.