#### Answer

The 6 values for $x_{i},y_{i}$ and for $0\leq x \leq1$ are shown in the table below

#### Work Step by Step

We are given $\frac{dy}{dx}=x-2xy$
so that $g(x,y)=x-2xy$
Since $x=0, y=1$
$g(x_{0},y_{0})=0$ and $y_{1}=y_{0}+g(x_{0},y_{0})h=1+0\times0.2=1$
Now $x_{1}=0.1, y_{1}=1$
and $g(x_{1},y_{1})=-0.1$
Then $y_{2}=1+(-0.1)\times0.2=0.96$
$y_{3}=0.886$
$y_{4}=0.794$
$y_{5}=0.7$
$y_{6}=0.62$