Find the particular solution to:
y" - 6y' + 9y = 17e^(3t)
(The homogeneous solution is y_1 = e^(3t), after finding the roots)
For the particular solution, I try:
y = Ae^(3t) ....... then y' = 3Ae^(3t)...... y" = 9Ae^(3t)
Substitute that in.....
9Ae^(3t) - 6(3Ae^(3t)) + 9(Ae^(3t)) = 17e^(3t)
9Ae^(3t) - 18Ae^(3t) + 9Ae^(3t) = 17e^(3t)
simplify this further, and everything on the left hand side cancels....which means
0 = 17e^(3t) which is not possible since e is asymptotic at y = 0.
What do I do!?
Same thing happens when I tried y = At(e^(3t)). Everything on the left hand side still cancels out after I substitute