Chapter 1.10, Problem 8P

For Problems $6-10$, use the modified Euler method with the specified step size to determine the solution to the given initial-value problem at the specified point. In each case, compare your answer to that obtained using Euler’s method.

The initial-value problem in Problem $3$.

For Problems $1-5$, use Euler’s method with the specified step size to determine the solution to the given initial-value problem at the specified point.

$3$. $y^{\prime }=x-y^2,y\left(0\right)=2,h=0.05,y\left(0.5\right)$.