This ODE is beyond the scope of the Student package. You get a better error message when expanding the product first:

Student:-ODEs:-ODESteps(expand(ode));
Error, (in Student:-ODEs:-OdeSolveOrder2) ODE is not supported

Check Tools -> Options -> Interface -> Large toolbar icons (first checkbox in the "Show" section).

I guess you want a space curve as follows:

plots:-spacecurve([t*sin(t), t*cos(t), 2/3*sqrt(2)*t^(3/2)], t=0..Pi);

To reproduce the graph from your screenshot, you will have to rotate the output a bit, or add options accordingly.

I'm too lazy for that. ;-)

By the way, since you asked for the length:

AL := VectorCalculus:-ArcLength(<t*sin(t), t*cos(t), 2/3*sqrt(2)*t^(3/2)>, t=0..Pi);

This is a good example for Maple's solve/identity feature:

Download: roots-wanted.mw

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The two linear equations you feed to solve are contradictory for f2. Check this in a separate step:

lineq1 := -2*A*xc - B*yc = D; lineq2 := -B*xc - 2*C*yc = E;
4*lineq1 + 3*lineq2;

For f1, they have a solution.

The use ... end use construct is newer than those control structures affected by interface(longdelim). One could think about introducing end as a short form for end use, but that would be counterproductive, as the recommendation is to use the long form for better readability.

I do not fully understand your question. You really should upload your worksheet to make it easier for others to help.

Anyway, here's my attempt. The algsubs command won't work because of the presence of sqrt. Fortunately, we can use subs here (simpler syntactic substitution), and by providing an assumption on c, we can simplify the result.

Please elaborate on the remaining steps of your draft.

Download ode-parameter-elimination.mw

Just supply the output=DataFrame option to the ExcelTools:-Import command. The default type is Matrix.

Please see the ?_ (or ?underscore) help page.

The command for grouping multiple terms into a common fraction is normal:

normal(e);

The defaults for scaletorange haven been improved in Maple 2023.

Independently of that, I suggest assigning A:=abs(j) (much shorter) and inserting another plot option: scaling=constrained (otherwise the circle looks too elliptic).

Download scaletorange-M23M24.mw

Color functions are available for 3D plots only.

This is fairly simple if we use the Matrix constructor along with your mapping (shown here in 1D Math aka Maple notation):

`ΔPV1` := Matrix(12, 8, (i, j) -> 100*(100*H0[i] - 100*H1[i,j])/((100 - H0[i])*H1[i,j]))

See the modified worksheet. I deleted some stuff at the end - perhaps you still need that, sorry. Also, I had to remove the absolute path from the Import call to make it work on my machine.

QuestionPrimes_TR.mw

Since your worksheet contains no dsolve call, it is unclear where your solution is coming from, and what assumptions on parameters are needed. However, the odetest result can be simplified as follows:

ot2 := odetest(G1, pde2);
simplify(ot2,'symbolic');

Note that the 'symbolic' option must be handled with care, as it may not be valid for all parameter values in the complex domain.