Please be very careful with writing down all calculations step by step and also explain all conclusions and results thoroughlyin words using mathematical language:
1. All solutions to the differential equation y'-2y=0 should also be solutions to the differential equation y''-ay'+ay=0. Determine the constant a such that this is true.
2. Determine if the inverse applies for this value of a, that is, if all solutions to y''-ay'+ay=0 are solutions to y'-2y=0.