@nm As Preben has observed, the problem on an arbitrary interval [a,b] may be translated to a problem on the interval [0,b-a].  Since Maple knows how to solve the latter problem, the solution to the former may be obtained by a simple substituion.  That's what I meant by writing that "it requires no extra effort".  The attached worksheet illustrates this.

heat-equation.mw

@nm Your analysis in report.pdf is correct up to equation (4).  The subsequent argument that leads to "So let us assume B = 0" is incorrect and therefore the rest of the calculations are invalid.

But you don't need to examine the calculations in order to tell that the final result is wrong.  You can tell that just by looking at your infinite series for u(x,t), a sample of which you have included in your post.  According to your calculations, u(x,t) is a sum of cosines regardless of the initial condition.  Since cosine is an even function, your u(x,t) is even in x.  But the correct solution need not be even in x because the initial condition can be anything.

I stand by my assertion that "Solving the PDE over an arbitrary interval [a,b] requires no extra effort".  I will write up the justification of that assertion and post it over the weekend.

@Gillee Thaks for the pointer.  Watching what Maple does with infolevel turned on, we see that is aware of the Fourier series but does not actually apply it.

@nm Maple knows how to solve the heat equation with Fourier series on the interval [0,L].  Solving it over an arbitrary interval [a,b] requires no extra effort.  I am puzzled why it's not programmed to do that.

@maxwell With these modified boundary conditions, Maple produces the exact solution through
pdsolve({pde, ic});
Adding boundary conditions confuses Maple.  I don't know why.

@nm The u(t,x) that you have proposed does not satisfy the boundary conditions.  It would have worked if the x domain were [-Pi/2 .. Pi/2].

@9009134 As I said before, if I were faced with solving such a problem, I will try first to find a simpler version of it which I am able to solve.  By a simpler version I don't mean a different set of parameters.  Rather, I mean a fundamentally reduced model, for example one that involves second order derivatives instead of the current model that involve sixth order derivatives.

I cannot do that for you because I have no idea what is behind these equations. Is it a physics problem?  If so, then it would be worthwhile to examine the assumptions that go into its mathematical model.  Generally, you may expect a coarser model to lead to lower order differential equations.  Do that one first, and only then attempt to solve the more complex version.

Anyway, that's what I would do if I were solving such a problem.

I use Maple on Xubuntu Linux and have no problem saving files in the normal way.  It's likely that there is a problem with your Maple's security settings, as acer has noted.  For your reference, here are two screenshots from my security settings.  Compare them with yours.

@vv You are correct on both counts.  Maple messes up the solution just as I did.  I wonder  whether there is any CAS at all that does this correctly.

@9009134 A boundary value problem is quite a delicate thing.  The solution must start at one end with just the right value and slope, and arrive at the other end again with just the right value and slope.  Sometimes this is possible, and sometimes it's not.  Do you have reason to believe that your boundary value problem has a solution?  Any calculation that mixes numbers of hugely varying magnitudes such as 10^(-7) and 10^5 in one equation raises a red flag in my mind.

Is there a simpler version of this problem that you can solve?  Perhaps that is the right place to start.  Do not attempt to solve a complex problem in one fell swoop. Establish your footing by solving a simple case first, then build upon it.

You have shown a picture of your expressions.  I can look at it but I cannot calculate with it.  You should post the actual text of your work, not just a picture.

The usual way to do that is to click the big fact green arrow which appears in your browser as you type your question, and upload your Maple worksheet.

To add the the worksheet to your existing post, click on "More..." at the bottom of the message and select Edit.  That will enable you to edit you current message, and will present you with the green arrow to enable you to upload your worksheet.

The title of your message is difficult to read.  It would be much more helpful if you would stick essential information such as that within the body of your message.  Here is what it says:

"unable to store %1 when datatype=%2",
    -9.65986559999997*10^(-7)+4.59993600000001*10^(-9)*((D@@5)(g))(1), float[8]

This indicates that dsolve() has encountered an expression involving the unevaluated expression D@@5)(g))(1) where it was expecting a number.  Examine your code to see why that happens.

Advice: For the ease of debugging, forget about the for bb ... loop for now.  Just do one single case and make it work.  The loop version can be done later.

@memdream Your most recent version has correct Maple syntax, however I have no confidence in its mathematical correctness, especially since you say that the calculations are meant to solve a problem in physics.

You know from elementary mathematics that an equation such as x² = 1 has two roots, x=±1.  Similarly, the equation x⁴ = −1 has four roots, which are x = ±sqrt(1/2) ± i sqrt(1/2).  The notation (−1)^1/4 is normally understood to refer to these four roots, collectively.

There are several occurrences of (−1)^1/4 in your equation.  Which of its four values do you expect to be used here?  Where does such an ambiguity enter your calculations?  You should check your physics model to see where these terms come from.

Plotting a graph of RV versus f is not difficult, as I will show below, but be warned that in view of what I have just explained, the result may be complete nonsense, especially in relation to your physics model.

OK here we go.  Let's call your equation eq.  We solve the equation for RV. Since the equation is 4th degree in RV, there are four solutions:
sol := solve(eq, RV):
Then sol[1] is the first solution, sol[2] the second, and so on.  Here is a plot of the real and imaginary parts of the first solution:
plot([Re(sol[1]), Im(sol[1])], f=100..4000, labels=[f, RV]);

You may plot the other three solutions in the same way.

@memdream In your expression there are several occurrences of terms like
   
What is that 9 doing at the end of that line?  Such errors are a common problem facing Maple's 2D-math-mode users.  I have added a note to the discussion in your previous question as to how to reconfigure Maple into 1D-math-mode.

@memdream Yes, it is worth trying, especially when I see that your next question suffers from 2D-math issues.  There you have several occurrences of terms like
   
which make no sense.  What is that 9 doing at the end of that line?

Consider configuring your Maple into a more usable form.  Instructions are here.

Beware that this reconfiguration will not fix your old worksheets—they are beyond repair.  It will apply to new worksheets that you create from scratch.  Furthermore, don't copy-and-paste from old sheets into the new, because the old 2D-math will contaminate the new one and your efforts will be wasted.