I appreciate that maple can solve equations so quickly, but i would like to solve the equation myself and only use the basic features of maple so that I can practice the theory. For example:

for the differential equation y'' + 3y' + 2y = 0 

I would like to assume y = ce^rt then plug it in and get something like

c*(r^2*e^rt + 3r*e^rt + 2e^rt) = 0

maple runs into problems regarding:

-whether the parameters are functions or constants