Chapter 1 - First-Order Differential Equations - 1.10 Numerical Solution to First-Order Differential Equations - Problems - Page 101: 9

$y(1)=0.711$

We have $$y'=-xy^2$$ Setting $h=0.2$ in equation $y'=-xy^2$ $$y_{n+1}=y_n-0.1(x^2_ny_n+x^2_{n+1}y_{n+1})$$ Hence, $y_1=0.996$ $y_2=0.9762$ $y_3=0.927$ $y_4=0.8382$ $y_5=0.711$ If we increase the step size to $h = 0.2$, the corresponding approximation to $y(1)$ becomes $y_{5}=0.711$