If I've read this correctly, the code beneath your image is

sum(x[j]*sum(y[i], i= k..n), j= k..n).

You ask for help to "solve" this. What does "solve" mean in this context? One usually solves equations or inequalities; the above is simply an expression. Do you mean simplify it, or find a closed form? That can't be done: The expression is too general.

Please upload the data file data1.csv.

@rolfjg I see now that you're working with a fairly old Maple (Maple 12). From the error message that you showed, I suspect that the datasetlabels option was added after Maple 12. I had no way of knowing that since the version where features are added is only very inconsistently mentioned in the help files.

I always would much rather have an actual command than something "interactive". So, try this (with both x and y being lists):

Statistics:-ColumnGraph(zip(`=`, x, y));

I'm 95% sure that this will work in Maple 12. If not, let me know, and I'll come up with something else.

@Markiyan Hirnyk This page implies that there's a MapleSim 7:  http://www.maplesoft.com/support/downloads/maplesim/msim7_01update.aspx

@tomleslie It's in the DTM worksheet. Look for it as the Greek letter, not spelled out.

I recommend that you never use the initialcondition command.

I've been using Maple for 16 years and answering questions about it online for nearly that long. I've answered many thousands of questions, and I've read the answers to many thousands more. Surely a few thousand of those questions have been about ODE systems. Yet in all that time I've never seen the initialcondition command. But, sure enough, I checked the help, and it exists. Clearly this command is not used in practice. And upon reading its minimal help file, I can see no practical use for it. Does anyone know what it's for? Is it part of some project/package that was never finished?

Your b[1], ..., b[4] are not differential equations: they contain no derivatives.

Yes, please upload your worksheet.

@acer I agree totally. Indeed, I almost added "However, I agree with Acer that that's not a good reason to avoid restart," but I didn't want to put words in your mouth.

Still, there may be other more-valid reasons to unassign all variables (or all variables of a certain type), and the above command is not-at-all obvious: Angle brackets are the only brackets that work.

@tomleslie Maple doesn't seem to have a problem plotting (in 2-D) things that get infinitely steep if you include the coordinateview option (or view option). For 3-D plots, it's a different story.

@dharr I think that coordinateview = [0..2, 0..Pi] may be closer to the OP's wishes.

By multiplying cos(t) and sin(t), you are converting to Cartesian coordinates. You don't want to do that if you're using the polarplot command. On the other hand, if you change your polarplot to simply plot and get rid of the coordinateview option (possibly replacing it with the view option), then you'll get a plot of a parametrized parabola in Cartesian coordinates.

@Rouben Rostamian  Yes, the solution produced by dsolve is much better analytically. But I tried several approaches, and I could not derive it myself.

On the other hand, I was able to derive my expression just using mental algebra.

@dharr Yes, I knew that entries didn't necessarily return the elements in order. And I knew that indexing to extract from the tables would make them take even longer. Sorry that I didn't mention that; I simply said "There are several other possibilities for the indexing." You see, I knew that the table methods were already slower than the Vector method, so I saw no need to go further because my point was to prove that the Vector method was faster.

@Axel Vogt But this Question isn't about plotting an inverse function. It's about plotting an implicitly defined function (with branch cuts).