@suvetha2000 You plots and symbolic solutions were correct, but your eigenvalues were not. You just copied the same matrix for all four cases---obviously that's wrong. Hopefully my Answer has given you some insight into computing eigenvalues. Don't use linalg for this or for anything else. Those commands were long ago replaced by more modern ones. Use the commands that I showed.

There are subtle differences between plots a and b and between c and d; none of the four are the same. The general shape and direction of these plots (often called phase portraits) can determined just from the signs and real/imaginary status of the eigenvalaues, and experts usually look at the eigenvalues first.

@suvetha2000 The matrix that you show in your Question---which is also the matrix that I used in my Answer---is correct. Off the top of my head, I don't know of a stock pre-coded method for reducing a high-order linear ODE to a first-order system in matrix form. I will see if I can find something though. There are a vast number of obscure commands (in DEtools and PDEtools) for manipulating ODEs.

So, you have a Normal distribution with mean 10 and standard deviation mu? That's pretty weird; is that what you really want?

@suvetha2000 Yes, that was the impresssion that I got from the instructions. But if you know how to do it in Maple also, then you can check your by-hand work.

@Christopher2222 Without me reviewing the whole thread, this is what I guess is happening: If you do this SVD trick on an n x m matrix, it's still an n x m matrix, it just has a much higher level of redundancy (or, equivalently, it has a much lower rank). But it still has n*m entries, so there's no savings if it's saved as a rectangular matrix. Try running a standard compression program, such as "zip", on both the SVD'd file and the original.

@Carl Love Here's my one-line minimal-arithmetic while loop. This uses Maple 2019 syntax:

{((b,a):= (0,1)), (while (s:= a+b) < 10000 do (a,b):= (s,a); if issqr(a) then a fi od)};

It was proven in 1964 that the only square Fibonacci numbers are 0, 1, and 144. See: Cohn, JHE (1964), "Square Fibonacci Numbers etc", Fibonacci Quarterly, 2: 109-13. The proof there is not exceedingly difficult.
 

@Stretto Regarding "collecting" on the strings: In my Answer, I provided a method for the mathematical evaluation (through the value command) of the colored output. Acer also gave a similar method. If that's not sufficient for your needs, then you'll need to be more explicit about what you mean by "collecting". The key component of these evaluations is the command Typesetting:-Parse. 

@suvetha2000 Apology accepted, and I'm available if you want to continue working on this problem.

I figured it out! The axis order is set by the DEplot3d command. Where you have [z(t), y(t), x(t)], you should make it [x(t), y(t), z(t)]. 

@Carl Love Sorry, the parabola is not showing up in that plot! I don't know why. It'll take me a little while to figure it out.

@goli You simply need to terminate the display command with a semicolon rather than a colon. The purpose of the colon is to suppress the output, which in this case is the plot itself.

display(a1, a2);

@goli Sorry, but I don't know the first thing about copy-and-pasting. I do all my work programmatically. Plots can be merged using the command plots:-display. There's probably a way to do it with copy-and-paste; I just know nothing about it except that it leads to corruption, moral decay, and irreproducible results; it's antithetical to the scientific method.

@vv Yes, that's what I meant. Note that all code in seq, add, and mul statements is invoked for every index value.

Alias allows an existing rtable to be indexed in a different way, without copying it. So it's not quite correct to say that it creates a 2x2 Matrix. Rather, it allows the 1-D Array created inside the Iterator to be indexed as a Matrix. 

@vv It's not quite the same thing, although it may ultimately produce the same output. The point of my form is to avoid repeated calls to Alias.

@Stretto Maple's normal order of evaluation---used in the vast majority of cases---is from the inside to the outside. This can be changed by procedures that declare parameters as uneval. This should be used rarely, and with caution. EV must be such a procedure. I am not familiar with it. What is it?

This works fine:

Color(ithprime(5));

I get a green 11.