Find the particular solution to
First, I found that the general solution is
So the list of terms that I obtain here is:
Now, for my guess of the particular solution, I have list of terms
Since I have repeats, I would take the derivative, so I have new list
So my particular solution is:
I know I'm missing something, I think I'm suppose to multiply x by one of the list, but I just can't remember what the method was, please help. Thanks.
Okay, I tried with this particular solution, but weird things happened:
After plugging in everything to the original equations, I have the following:
So I have
But I don't have anything on the left to equal to the 1 on the right, what am I doing wrong? I really feel stupid now because I'm actually tutoring this class, I took DEQ like 3 years ago, I JUST CAN'T UNDERSTAND WHY I AM NOT GETTING THIS RIGHT AS A GRADUATE STUDENT!!!!
Perhaps I need because of the constant term in the RHS?
This is how to find the particular solution corresponding to the term on the RHS of the DE.
To find the particular solution corresponding to the constant term on the RHS of the DE you try one of the form y = a and get a = -1/3.
Then you add these two particular solutions together to get the overall particular solution.