Chapter 6.1, Problem 81E

Euler's Method In Exercises 79-81, complete the table using the exact solution of the differential equation and two approximations obtained using Euler’s Method to approximate the particular solution of the differential equation. Use $h=0.2$ and $h=0.1$ , and compute each approximation to four decimal places.

x	0	0.2	0.4	0.6	0.8	1
y(x) (exact)
$\begin{array}{l}y(x)\\ (h=0.2)\end{array}$
$\begin{array}{l}y(x)\\ (h=0.1)\end{array}$

Differential Equation Initial Exact Condition Solution

$\frac{dy}{dx}=y+\cos x$ $(0,0)$ $y=\frac{1}{2}(\sin x-\cos x+e^x)$