Use the pertubation expansion approximation

$x=x0+lonx1+lo{n}^2$

to separate the equation $\frac{d^2}{d{t}^2}+K\frac{dx}{dt}+w^{2}x=$Fcos$t.$ into three simple equations, namely $1.\frac{d^{2}x0}{d{r}^2}=f1,2.\frac{d^{2}x1}{d{r}^2}=f2,3*\frac{d^{2}x2}{d{r}^2}=f3$ That is$,$ establish $f1,f2$ and $f3.$