Answer
$y(0.6)= y_{7}=1.1676$
Work Step by Step
We are given $\frac{dy}{dx}=x+\sqrt y$
so that $g(x,y)=x+\sqrt y$
Since $x=0, y=1$
$g(x_{0},y_{0})=1$
and $y_{1}=y_{0}+g(x_{0},y_{0})h=1+1\times0.1=1.1$
Now $x_{1}=0.1, y_{1}=1.1$ and $g(x_{1},y_{1})=1.149$
Then $y_{2}=1+1.149\times0.1=1.115$
$y_{3}=1+(1.256)\times0.1=1.1256$
$y_{4}=1+(1.361)\times0.1=1.1361$
$y_{5}=1+(1.466)\times0.1=1.1466$
$y_{6}=1+(1.571)\times0.1=1.1571$
$y_{7}=1+(1.676)\times0.1=1.1676$
$y(0.6)= y_{7}=1.1676$
