how to solve a non-homogeneous equation? I do not like to guess, is there another way I can solve these equations?

Question

anonymous · Answer

equation?

myininaya · Answer

yes you cannot solved every differential equation the same way

math007 · Answer

y"-2y'-3y=3e^2x

myininaya · Answer

first let's pretend it is homogeneous.  so we have r^2-2r-3=0 which gives r=-1 and r=3 so we have y=Ae^(3t)+Be^(t) for any constant.  But this doesn't solve the homogeneous solution.  So the only way I know how to solve this differential equation is to choose y=Ae^(2t) and find what A is.  But this is that guessing thing you were talking about.

myininaya · Answer

oops y=Ce^(3t)+Be^(-t)

math007 · Answer

yes, I understand this much. Now the problem is finding the right side, the non homog. part. How do I go about solving the right side?