Originally Posted by

**ecMathGeek** I figured out how to do this. I simply expanded the differential operator AL and showed that after plugging in e^(rt), the form of the auxiliary equatoin has the same form as that of the expanded operator, and thus when factored, the auxiliary equation will have the same form as the factored form of the operator.

After figuring this out, I came across something else I cannot explain.

Apparently I need to show how the factored from of the auxiliary equation will take the form:

s_{k}*[(r - a)^2 + b^2]^(u + K + 1)*(r - **r_{2u+1}**)***(r - **r_{k}**) = 0

where r_{2u+1},...,r_{k} are the remaining roots of the auxiliary equation after factoring out the "u" complex roots. I have no clue where r_{2u+1} or r_{k} come from. I might eventually figure this out, but right now I'm stumped.