Answer
$y(0.6)$ mean $x=0.6 \rightarrow y_{7} \approx 2.333$
Work Step by Step
We are given $\frac{dy}{dx}=1+y$
so that $g(x,y)=1+y$
Since $x=0, y=2$
$g(x_{0},y_{0})=1+2=3$
and $y_{1}=y_{0}+g(x_{0},y_{0})h=2+3\times0.1=2.3$
Now $x_{1}=0.1, y_{1}=2.3$ and $g(x_{1},y_{1})=1+2.3=3.3$
Then $y_{2}=2+3.3\times0.1=2.33$
$y_{3}=2+(3.33)\times0.1=2.333$
$y_{4}=2+(3.333)\times0.1=2.3333$
$y_{5}=2+(3.3333)\times0.1=2.33333$
$y_{6}=2+(3.33333)\times0.1=2.333333$
$y_{7}=2+(3.333333)\times0.1=2.3333333$
$y(0.6)$ mean $x=0.6 \rightarrow y_{7}=2.3333333 \approx 2.333$
