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Here is the question:
I have posted a link there to this topic so the OP can see my work.The differential equation
\(\displaystyle y''+2y'+y=0\)
has linear independent solutions $e^{-x}$ and $xe^{-x}$. Pretend you only know that $xe^{-x}$ is a solution, and use reduction of order to obtain a second linearly independent solution.