- #1
Mechdude
- 117
- 1
Homework Statement
i have this problem
[tex] y'' - y' - 2y= -6xe^{-x} [/tex]
Homework Equations
this is the homogenous solution : [tex] y_{h}= c_{1} e^{-x} + c_{2} e^{2x} [/tex]
The Attempt at a Solution
first i can do the problem but what is perplexing me is why of these two tentative particular solutions the latter is chosen, [tex] y_{p1}= Axe^{-x} [/tex][tex]
y_{p2}= x(A + Bx)e^{-x} [/tex]
the former leads to an impossible situation but none the less its not appearing in the homogenous solution , the latter looks like the choice made when the roots of the auxilliary equation of the differential equation are real and the same , but in this case they are not real and the same , but this is what works , why would one choose the latter?