@brian bovril Thanks for your answer. I was wondering if it was possible to integrate both the iterated integrals with a particular rule (I chose Trapezoid arbitrarily). I assume there is a way to do this, since if we do not specify a method, I believe the first iterated integral that is calculated uses whatever the default method is.

@Preben Alsholm Thanks for your assistance. At first I thought I was just messing the code up, but I guess my omega value was just too high. Checking the spectral radius was a good idea. What a great detailed answer!

@acer The question in the textbook had 2 parts. One with the [1,3] entry as a -1, and the other part had it as a -2. I was trying the code for both of them. For the -1, the code ran successfully, but with the -2, I get an error- something about exceeding iteration number.

Nevermind- forgot to capitalize "m" and "v". Thanks for your help!

@acer I'm still getting an error. Any idea where my mistake could be?

My code is as follows:

with(Student[NumericalAnalysis])

A := matrix([[1, 0, -1], [-.5, 1, -.25], [1, -.5, 1]])

b := vector([.2, -1.425, 2])

LinearSolve(A, b, maxiterations = 300, method = jacobi, tolerance = 10^(-2))

Thanks, I will try that. I was trying to do this, but was getting error messages:

IterativeApproximate(A, b, maxiterations = 300, method = jacobi)

The interval is [-5,5]

Apologies- the code should read as follows:

f := proc (x) options operator, arrow; exp(x)*cos*x end proc

s2 := taylor(f(x), x = (1/3)*Pi, 2)

p2 := convert(s2, polynom)

y1 := evalf(subs(x = .5, f(x)))

y2 := evalf(subs(x = .5, p2))

Also, the default method does not look like the Forward Euler method, so I was wondering if anybody knew what method is used by default?

@acer  When I run the code, it a window that says "explore" pops up and asks me to fill out some stuff. Should I just leave it with the default values in the window?

I made a mistake when I typed it out. It should be: 

(dy(t))/(dt)=t(1-0.3t)-(ty)/(1+0.6t)

@Britzel I don't think there is a way to mark a question as answered. (Someone correct me if I'm wrong.)

@Kitonum Hi, thanks for your answer. I'm still learning Maple, so may I ask what " '$'(1,6) " does in the thickness option?

@Carl Love Thanks for your answer. I was just wondering if there was a way to solve the problem without the use of the Orthogonal Expansions package. 

I can't edit yet, but I forgot one thing. I also need the graph to be the domain and range I defined in my code above, that is x between 0 and 3 (including 0 and 3) and y between -2 and 2 (including -2 and 2).