Given that,

is the auxiliary equation associated with the linear differential equation

what is the form of a particular solution

DO NOT EVALUATE THE COEFFICIENTS IN

We have these 2 general rules that we follow to determine the form of the particular solution of a nonhomogenous L.D.E. with constant coefficients.

We look at each of the pieces not part ,

i.e.

The only part I was confused about is the "1" term in the RHS of the differential equation.

How do we apply our "rules" to this piece?

Also, if someone could quickly check my work that'd be great!(See figure attached)

Thanks again!