@acer Thanks alot. The last one was what I was looking for :D

@nm Thanks alot, made sense. The result was very identical, except for an arithmetic.

Here's our solution versus lecturer's:

Maple code:

OwnCalculation: (calculation)
D(x)(t) = Vector[column](2, [diff(x__1(t), t), diff(x__2(t), t)]) and Vector[column](2, [diff(x__1(t), t), diff(x__2(t), t)]) = Vector[column](2, [x__1(t) - x__2(t) - 3, 12*x__1(t) - 8*x__2(t) + 4])

Lecturer: (only result)
D(x)(t) = Typesetting:-delayDotProduct(Matrix(2, 2, [[1, -1], [12, 8]]), x(t), true) + Vector[column](2, [-3, 4]);

Is there another way to set up something from an equation to a matrix? More like an output like the above one?

Thanks for your time and help, it is appreciated :D

@Carl Love 

Another question :-) Can I, based on the command, write a 2nd and 4th order Taylorpolynomial with developmentpoint 0 on the interval e.g. [0, 1000], by using odeplot?

Because I know the format below is not correct according to my question, but is there a way to do it?

@acer 

I just added it, won't do it again sorry, that's why I added it.

@Carl Love 

Thanks for the advice, it helped, and the result looks more clear and manageable now. 

Also got the numeric option to work :D

@Carl Love 

Honestly, my intention when deleting the question was not in a bad way, it's just to show that the problem is solved.

But clearly, I agree and I see the point to keep it, and not delete it, as people really try to help, and perhaps other people will find this useful. I'm really sorry for that. I will add the question now.

@Carl Love 

Ohh my bad, forgot those, the both are constants. Thanks for the help, I have now added both constants, but now an error occurs from dsolve();.

Am I missing something?

@Carl Love 

Thanks for the answer :-)
I have values for the constants and functions. In relation to what is in the assignment, I should define the functions and constants and only use the function dsolve();

And as you mentioned, I get no response from dsolve ;(

@nm 

Thank you, yes I have entered that, thanks for the advice :)