Use a CAS to explore graphically each of the differential equations. Perform the following steps to help with your explorations.

a. Plot a slope field for the differential equation in the given $x y$ -window.

b. Find the general solution of the differential equation using your CAS DE solver.

c. Graph the solutions for the values of the arbitrary constant $C=-2,-1,0,1,2$ superimposed on your slope field plot.

d. Find and graph the solution that satisfies the specified initial condition over the interval $[0, b]$

e. Find the Euler numerical approximation to the solution of the initial value problem with 4 subintervals of the $x$ -interval, and plot the Euler approximation superimposed on the graph produced in part (d).

f. Repeat part (e) for $8,16,$ and 32 subintervals. Plot these three Euler approximations superimposed on the graph from part (e).

g. Find the error ( $y$ (exact) $-y$ (Euler)) at the specified point $x=b$ for each of your four Euler approximations. Discuss the improvement in the percentage error.

$$\begin{aligned}&y^{\prime}=x+y, \quad y(0)=-7 / 10 ; \quad-4 \leq x \leq 4, \quad-4 \leq y \leq 4\\&b=1\end{aligned}$$