1. The problem statement, all variables and given/known data We are just starting to learn about basic differential equations in Calc 2 and I learned about separable differential equations but I'm not familiar with this style, here's the question: Given the differential equation of the form ay"+by'+y=0, find constants a and b so that both y=e^x and y=e^(2x) are solutions. 2. Relevant equations None really 3. The attempt at a solution To be honest I have thought about this a lot and I'm not exactly sure where to start. I can't see how you could use separable differentials to solve this one and I really am not too sure how to "solve" it. I was thinking about taking the integral of both sides but I'm not sure that would be a correct operation since there is no "dy". I'm also not exactly sure how you could solve that equation to get e^x in the first place so I'm pretty lost on this one.