Given that $x_1(t)=1$ and $x_2(t)=e^{-2t}$ are the solutions of the differential equation

$x^{\text{'}\text{'}}+x^{\text{'}}+x=0$

where $$ and $$ are real constants, find $$ and $.$ For these values of $$ and $,$ find the particular

solution of the differential equation

$x^{\text{'}\text{'}}+x^{\text{'}}+x=4+(t+1)e^{-2t}.$