Maple Tool 3

This tool is designed to be used with Exercise 19 in Section 5.3.

Enter your formula for the derivative, yprime.  Your formula should involve both x and y.

>	yprime:=(x,y)->???;

The following steps carry out the iteration and plot the numerical solution.

>	n:=10; Delta:=1/n; x:=k->k*Delta; Y := proc(k)

>	Y(k) := evalf(Y(k-1)+yprime(x(k-1),Y(k-1))*Delta);

>

end:

>	Y(0):= 0: solution:=[seq([x(k),Y(k)],k=0..n)]:

>	solPlot := plot(solution, x=0..1, y=0..1, style=POINT,symbol=circle, color=blue, thickness=2):%;

>

Compare the left and right sides of the defining equation at x = 1:

>	sin(1.0)*cos(Y(n)); Y(n);

>