Originally Posted by

**plopony** 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)

(simplified)

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!?

(edit)

Same thing happens when I tried y = At(e^(3t)). Everything on the left hand side still cancels out after I substitute