Second order linear differential equations : Particular Integral 
How do they find the particular Integral. These two lines are not giving me any clue. Please someone explain me.


The method of variation of parameters, however, provides one extra term.
$y_p=-\frac{1}{4}\mathrm{e}^{-2x}+\frac{x}{2}\mathrm{e}^{-2x}$
Solution Procedure:
Two fundamental solutions are $y_1(x)=\mathrm{e}^{-2x}$ and $y_2(x)=\mathrm{e}^{-4x}$.
Thus, $y_p=y_2(x)\int\frac{y_1(x)f(x)}{W(y_1,y_2)}\mathrm{d}x-y_1(x)\int\frac{y_2(x)f(x)}{W(y_1,y_2)}\mathrm{d}x$
where, $W(y_1,y_2)=y_1(x)y_2'(x)-y_1'(x)y_2(x)$ and $f(x)=\mathrm{e}^{-2x}$.
