Answer
The 6 values for $x_{i},y_{i}$and for $0\leq x \leq 1$ are shown in the table below
Work Step by Step
We are given $\frac{dy}{dx}=y$
so that $g(x,y)=y$
Since $x=0, y=1$
$g(x_{0},y_{0})=1$ and $y_{1}=y_{0}+g(x_{0},y_{0})h=1+1\times0.2=1.2$
Now $x_{1}=0.1, y_{1}=1.2$
and $g(x_{1},y_{1})=1.2$
Then $y_{2}=1.2+1.2\times0.2=1.44$
$y_{3}=1.728$
$y_{4}=2.074$
$y_{5}=2.488$
$y_{6}=2.986$