I am doing some studying regarding Differential Equations and using the Method of Undetermined Coefficients in order to solve second order, non-linear, non-homogeneous equations. While asking this question, I realized someone had already asked the same question regarding the same exact problem on stackexchange. Their question can be found here.
The question that I have is asking us to solve:
$y'' -2y' -3y = (-3t)(1/e^t)$ , (call this $\alpha$).
The answer to $\alpha$ in the textbook is the same as what user32240 said, and then the coefficients are also listed in his/her answer.
Thus far, I have looked at the following link (if you visit this link, page 15 is the area with the information regarding this problem), and I have made little progress to see why we are using:
$(At^2)(1/e^t)+(Bt)(1/e^t)$, (call this $*$).
My Question is:
Why are we using $*$ to solve this equation? While I am attempting to solve $\alpha$, I am using $*/t$. Any help would be much appreciated!
TITLE: Elementary Differential Equations and Boundary Value Problems EDITION: Tenth Authors: William E. Boyce / Richard C. DiPrima Question: pg.184, question 5