Try
CB
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!
I was confused about that 1 on the RHS of the equation, I wasn't really sure if I had to look at it or not.
If I assume I do,
Is 1 part of ? Yes, it is.
So by rule 2,
is part of , but we already have this piece in so I shouldn't be including it in .
Can you see why I get confused when we work with that piece? Hopefully you can clarify my confusion.
EDIT: Here are the two rules as per my textbook. (See figure attached)
I can not make sense of your rules (I expect I could if I sent fifteen minutes on them, but the dog is waiting for his walk) , but you cannot ignore the 1 on the right, and inspection shows that what I posted above is a particular integral corresponding to a 1 on the right.
CB
Does anyone else care to share their input?
I'm not doubting what you've said CB, it seems you know what you're doing, but in the course I'm currently taking we haven't learnt about any of those things and these two "rules" are all I have to go off.
I have to try to make sense of things with the knowledge I've be taught throughout the course.