Question

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

Answer 1

equation?

Answer 2

yes you cannot solved every differential equation the same way

Answer 3

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

Answer 4

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.

Answer 5

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

Answer 6

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?