@tomleslie It must be that R is the foxes and K is the rabbits. The letters might come from another language. The equilibrium is K = a/b,  R = c/b/e. With the given parameter values, that's 200 and 15.

@primogen How can you know whether the command worked or not without looking at its output? Your most-recent worksheet indicates that you didn't look in the Matrix dMM_t, and I see no error message.

@JackLe Acer has shown the use of the official transpose operator: (...)^%T , which can be used with official Matrices and Vectors. It can also be (...)^+. 

@primogen I'm surprised, but maybe it's a version difference. It worked in my Maple 2018. I see that you're using Maple 2017. Try

dMM_t:= diff~(MM_t, t);

Putting a tilde ~ after any operator makes it elementwise, but many commands are automatically elementwise, such as, apparently Maple 2018's diff.

If that doesn't work, post the executed worksheet showing the contents of MassMatrix.

What you call "assignments" above are actually just equations, although I see that you tried to use the assignment operator := in your worksheet. That's not allowed. Just use =. They won't be used automatically. You can apply specific simplifications with the simplify command at the point where they're needed. But let's deal with that later, after the diff is fixed. Just the generic simplify would probably handle this case anyway.

Could you post the recurrence equations and the initial conditions? I think that you either switched the roles of K and R somewhere or that you switched a plus/minus sign somewhere. I say this because after I corrected your program above, I still can't get convergence to an equilibrium (other than [0,0]) for any initial conditions that I try.

@primogen Your Matrix actually contains theta[1], ..., theta[4]. I could give you a subs command that handled every theta, but this process of making a substitution for every subexpression of a certain type is common enough that there's a separate command for it: subsindets. (It's my favorite top-level Maple command.) So,

MM_t:= subsindets(MassMatrix, specindex(theta), T-> T(t)):
dMM_t:= diff(MM_t, t):

To see what the specindex(theta) means, do

indets(MassMatrix, specindex(theta));

It's the set of all indexed forms of theta that occur in the matrix. The T-> T(t) explains what to substitute for each element of that set. The specindex(theta) is not itself a command; it's something called a type. 

@primogen Yes, you can differentiate a matrix. Indeed, any operation can be applied elementwise to all of the elements in a container (such as a Matrix).

I haven't looked at your worksheet yet.

@Earl Thanks, I'm well known for coming up with the explanation that is best for each individual student. Though, of course, this works better in person. The technique that I used is called "logarithmic differentiation", and you should be able to look that up either online or in a textbook. It can be used for a variety of other complicated expressions as well as a(x)^b(x).

@primogen Please post your worksheet by using the green uparrow that's on the top line of the toolbar of the MaplePrimes editor.

@primogen expr is my name for whatever your expression/equation is. Go to the command line that generates your expression that you want to differentiate. Begin that command line with expr :=  .  This operation is called assignment; it's the most fundamental operation in most computer languages. You can (and should!) replace my expr with whatever name is actually meaningful for your situation.

@torabi Your syntax issue is due to the curly braces { } that you used in the assignment to ICs. Get rid of them. The plot specification should be [t, Z(t)], not [t,v], which'll just plot a constant as we discussed already. 

After that, there are convergence issues. I think that you are misinterpretting that PDF. You seem to think that V(t) and v are the same thing. That seems pretty strange to me. And what happened to lambda= 0.11?

@ainsyah The numeric solution of BVPs of this type (nanofluid related) is one of the most commonly asked Questions on MaplePrimes, and searching the archives should turn up hundreds of posts (although, I have to admit, the search feature of MaplePrimes is a very bad search engine, and hence I rarely use it). I just wrote a very long Post on this topic three days ago. It is currently the second-most-recent Post (in the Recent Posts section).

Please read that Post and download the worksheet. Make a copy of the worksheet with a scratch name. Open that in Maple. Try to follow my format for entering the ODE, the BCs, etc. Just practice with that at this point. Don't worry about solving yet. I'll be awake for a few hours probably, so post your worksheet as soon as your improvement of it and your learning starts to slow down significantly. If you have specific questions, type them right in the worksheet.

You are missing one boundary condition.

I don't know much about the symbolic solution of this type of problem. I'm amazed that it's possible at all when all the parameters are symbolic, or even numeric but nonzero.

@Ronan You are using y on the left side of the equation, but Y as an argument to collect; whereas Christian used Y in both places.

Could you post a screenshot showing any of the above expressions in actual use, either as input or output?

@torabi Well? I'm not going to type those equations into Maple. You type them, then I'll help.

My theoretical knowledge of electricity is small, but I think that what you show as V(constant) should be 0, i.e., the voltage varies sinusoidally between -3 volts and +3 volts. If I am wrong about that, then you'll need to either specify the constant part, or give one more initial (t=0) or boundary (t = b, b <> 0) condition for Z or Z' (or a condition combining Z and Z').